Elementary Statistics for Business

Identify whether the statement describes inferential statistics or descriptive statistics.

There is a relationship between smoking cigarettes and getting emphysema.

inferential statistics
From past figures, it is predicted that 19% of the registered voters in California will vote in the June primary.
descriptive statistics
Determine whether the data are qualitative or quantitative.

the number of seats in a movie theater

quantitative
Identify the data set’s level of measurement.

hair color of women on a high school tennis team

nominal
Identify the data set’s level of measurement.

number of milligrams of tar in 85 cigarettes

ratio
Identify the data set’s level of measurement.

the ratings of a movie ranging from “poor” to “good” to “excellent”

ordinal
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Identify the data set’s level of measurement.

the final grades (A, B, C, D, and F) for students in a statistics class

ordinal
Identify the data set’s level of measurement.

the nationalities listed in a recent survey (for example, Asian, European, or Hispanic).

nominal
Identify the data set’s level of measurement.

manuscripts rated “acceptable” or “unacceptable”

ordinal
Identify the data set’s level of measurement.

the lengths (in minutes) of the top ten movies with respect to ticket sales in 2007

ratio
Decide which method of data collection you would use to collect data for the study. Specify either observational study, experiment, simulation, or survey.

A study where a drug was given to 23 patients and a placebo to another group of 23 patients to determine if the drug has an effect on a patient’s illness

experiment
Decide which method of data collection you would use to collect data for the study. Specify either observational study, experiment, simulation, or survey.

A study where you would like to determine the chance getting three girls in a family of three children

simulation
Identify the sampling technique used.

Every fifth person boarding a plane is searched thoroughly.

systematic
Identify the sampling technique used.

A researcher for an airline interviews all of the passengers on five randomly selected flights.

cluster
Identify the sampling technique used.

A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers.

random
Identify the sampling technique used.

A market researcher randomly selects 200 drivers under 55 years of age and 200 drivers over 55 years of age.

stratified
Identify the sampling technique used.

A researcher randomly selected 25 of the nation’s middle schools and interviewed all of the teachers at each school.

cluster
Solve the problem.

The average age of the students in a statistics class is 22 years. Does this statement describe:

descriptive statistics?
Solve the problem.

Based on previous clients, a marriage counselor concludes that the majority of marriages that begin with cohabitation before marriage will result in divorce. Does this statement describe inferential statistics or descriptive statistics?

inferential statistics
Solve the problem.

Classify the number of seats in a movie theater as qualitative data or quantitative data.

quantitative data
Solve the problem.

Identify the level of measurement for data that are the temperature of 90 refrigerators.

interval
Solve the problem.

Identify the level of measurement for data that are the number of milligrams of tar in 79 cigarettes.

ratio
Solve the problem.

Identify the level of measurement for data that are the ratings of a movie ranging from poor to good to excellent.

ordinal
Solve the problem.

Identify the level of measurement for data that are the nationalities listed in a recent survey (for example, Asian, European, or Hispanic).

nominal
Solve the problem.

The numbers of touchdowns scored by a major university in five randomly selected games are given below. Identify the level of measurement.

1 5 4 5 5

ratio
Solve the problem.

What method of data collection would you use to collect data for a study where a political pollster wishes to determine if his candidate is leading in the polls?

use sampling
Solve the problem.

At a local community college, five statistics classes are randomly selected and all of the students from each class are interviewed. What sampling technique is used?

cluster
Solve the problem.

A community college student interviews everyone in a statistics class to determine who owns a car. What sampling technique is used?

convenience
Solve the problem.

A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers. What sampling technique was used?

random
Solve the problem.

A market researcher randomly selects 200 drivers under 35 years of age and 100 drivers over 35 years of age. What sampling technique was used?

stratified
Solve the problem.

The names of 70 contestants are written on 70 cards. The cards are placed in a bag, and three names are picked from the bag. What sampling technique was used?

random
Solve the problem.

What method of data collection would you use to collect data for a study where you would like to determine the chance getting three girls in a family of three children?

use a simulation
Use the given frequency distribution to find the
(a) class width.
(b) class midpoints of the first class.
(c) class boundaries of the first class.

Phone Calls (per day)

(a) 3
(b) 9.5
(c) 7.5-11.5

(a) 3
(b) 10.5
(c) 8-11

(a) 4
(b) 10.5
(c) 8-11

(a) 4
(b) 9.5
(c) 7.5-11.5

a) 4
(b) 9.5
(c) 7.5-11.5
Provide an appropriate response.

Use the ogive below to approximate the cumulative frequency for 24 hours.

Student Answer:
75
27
17
63

63
For the given data , construct a frequency distribution and frequency histogram of the data using five classes. Describe the shape of the histogram as symmetric, uniform, skewed left, or skewed right.

Data set: California Pick Three Lottery

8 6 7 6 0 9 1 7 8 4
1 5 7 5 9 7 5 3 9 9
8 8 3 9 8 8 9 0 2 7

skewed right
symmetric
uniform
skewed left

Skewed Left
Provide an appropriate response.

Use the histogram below to approximate the mode heart rate of adults in the gym.
a) 70
b) 2
c) 55
d) 42

70
Provide an appropriate response.

The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the median speed.

118.1 202.2 190.1 201.4 191.3 201.4 192.2 201.2 193.2 201.2 194.5 199.2 196.0 196.2

195.8
201.2
196.7
196.1

196.1
Provide an appropriate response.

The scores of the top ten finishers in a recent golf tournament are listed below. Find the median score.

67 67 68 71 72 72 72 72 73 76

72
Provide an appropriate response.

Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = O. Grades are weighted according to credit hours. If a student receives an A in a four-unit class, a D in a two-unit class, a B in a three-unit class and a C in a three-unit class, what is the student’s grade point average?

2.75
Provide an appropriate response.

The lengths of phone calls from one household (in minutes) were 2, 4, 6, 7, and 8 minutes. Find the midrange for this data.

2 minutes
5 minutes
6 minutes
10 minutes

5 min
Provide an appropriate response.

Find the range of the data set represented by the graph.

6
20
5
17

6
Provide an appropriate response.

Find the sample standard deviation.

2 6 15 9 11 22 1 4 8 19

7.1
Provide an appropriate response.

The mean score of a placement exam for entrance into a math class is 80, with a standard deviation of 10. Use the Empirical Rule to find the percentage of scores that lie between 60 and 80. (Assume the data set has a bell-shaped distribution.)

95%
34%
47.5%
68%

47.5%
Provide an appropriate response.

The mean score of a competency test is 77, with a standard deviation of 4. Use the Empirical Rule to find the percentage of scores between 69 and 85. (Assume the data set has a bell-shaped distribution.)

95%
68%
50%
99.7%

95%
Provide an appropriate response.

The mean SAT verbal score is 478, with a standard deviation of 98. Use the Empirical Rule to determine what percent of the scores lie between 380 and 478. (Assume the data set has a bell-shaped distribution.)

34%
47.5%
68%
49.9%

34%
Use the grouped data formulas to find the indicated mean or standard deviation.

The manager of a bank recorded the amount of time a random sample of customers spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Approximate the sample mean. Round your answer to one decimal place.

9.0
13.5
9.2
7.7

9.2
Use the grouped data formulas to find the indicated mean or standard deviation.

A random sample of 30 high school students is selected. Each student is asked how many hours he or she spent on the Internet during the previous week. The results are shown in the histogram. Estimate the sample mean.

8.1
8.3
7.9
7.7

7.9
Provide an appropriate response.

In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed below.

a) If a constant value k is added to each value, how will the standard deviation be affected?

b) If each value is multiplied by a constant k, how will the standard deviation be affected?

1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8

The standard deviation will not be affected.
The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find Q1.

154 156 165 165 170 171 172 180 184 185
189 189 190 192 195 198 198 200 200 200
205 205 211 215 220 220 225 238 255 265

180
Provide an appropriate response.

Find the z-score for the value 55, when the mean is 58 and the standard deviation is 3.

z = 0.90
z = -0.90
z = -1.00
z = -1.33

z= -1.00
Provide an appropriate response.

The test scores of 30 students are listed below. Find P30.

31 41 45 48 52 55 56 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 85 87 90 92 95 99

67
56
90
63

63
Provide an appropriate response.

A teacher gives a 20-point quiz to 10 students. The scores are listed below. What percentile corresponds to the score of 12?

80 8 10 7 15 16 12 19 14 9

13
12
25
40

40
Solve the problem.

The scores of the top ten finishers in a recent LPGA Valley of the Stars Tournament are listed below. (Source: Los Angeles Times)

71 67 67 72 73 68 72 72

Find the mode score.
67
73
72
76

72
Solve the problem.

The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the median speed.

181.1 202.2 190.1 201.4 191.3 201.4 192.2 201.2 193.2 201.2 194.5 199.2 196.0 196.2

201.2
192.2
196.7
196.1

196.1
Solve the problem.

For the following data set, approximate the sample standard deviation of phone calls per day.

8-11 18
12-15 23
16-19 38
20-23 47
24-27 32

2.9
18.8
3.2
5.1

5.1
Solve the problem.

Find the range of the data set represented by the graph.

20

15

10

5

0 1 2 3 4 5 6 7

a) 20
b) 17
c) 6
d) 5

c) 6
Solve the problem.

Find the z-score for the value 70, when the mean is 76 and the standard deviation is 2.

z= -.89
z= -3.00
z= .89
z= -3.50

z= -3.00
Solve the problem.

The average IQ of students in a particular calculus class is 110, with a standard deviation of 5. The distribution is roughly bell-shaped. Use the Empirical Rule to find the percentage of students with an IQ above 120.

2.5%
11.15%
15.85%
13.5%

2.5%
Solve the problem.

The ages of 10 grooms at their first marriage are listed below. Find the midquartile.

35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9

43.7
34.5
34.1
34.2

34.2
Solve the problem.

For the mathematics part of the SAT the mean is 514 with a standard deviation of 113, and for the mathematics part of the ACT the mean is 20.6 with a standard deviation of 5.1. Bob scores a 660 on the SAT and a 27 on the ACT. Use z-scores to determine on which test he performed better.

ACT
SAT

SAT
Solve the problem.

For the following data, approximate the mean number of phone calls per day.

8-11 31
12-15 34
16-19 28
20-23 30
24-27 6

16
15
14
26
17

16
Solve the problem.

For the following data, approximate the mean number of phone calls per day.

8-11 48
12-15 16
16-19 42
20-23 34
24-27 45

18
16
37
19
17

18
Solve the problem.

A student receives test scores of 62, 83, and 91. The student’s final exam score is 88 and homework score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is 15% of the final grade. What is the student’s mean score in the class?
90.6
76.6
80.6
85.6

80.6
Solve the problem.

The grade point averages for 10 students are listed below. Find the range of the data.

2.0 3.2 1.8 2.9 .9 4.0 3.3 2.9 3.6 .8

3.2
1.4
2.45
2.8

3.2
Solve the problem.

A competency test has scores with a mean of 69 and a standard deviation of 4. A histogram of the data shows that the distribution is normal. Use the Empirical Rule to find the percentage of scores between 61 and 77.

95%
68%
99.7%
50%

95%
Solve the problem.

SAT verbal scores are normally distributed with a mean of 446 and a standard deviation of 91. Use the Empirical Rule to determine what percent of the scores lie between 355 and 446.

47.5%
34%
68%
49.9%

34%
Solve the problem.

SAT verbal scores are normally distributed with a mean of 426 and a standard deviation of 94. Use the Empirical Rule to determine what percent of the scores lie between 332 and 426.

49.9%
34%
68%
47.5%

34%
Solve the problem.

SAT verbal scores are normally distributed with a mean of 450 and a standard deviation of 100. Use the Empirical Rule to determine what percent of the scores lie between 250 and 550.

83.9%
68%
34%
81.5%

81.5%
Rank the probabilities of 10%, 1/5, 0.06 from the least likely to occur to the most likely to occur.

0.06, 10%, 1/5
0.06, 1/5, 10%
10%, 1/5, 0.06
1/5, 10%, 0.06

0.06,10%, 1/5
A coin is tossed. Find the probability that the result is heads.

.1
1
0.5
0.9

.5
Solve the problem.

If an individual is selected at random, what is the probability that he or she has a birthday in July? Ignore leap years.

31/365
1/365
12/365
364/365

31/365
Solve the problem.

The distribution of blood types for 100 Americans is listed in the table. If one donor is selected at random, find the probability of selecting a person with blood type A+ or A-.

Blood type: o+ o- A+ A- B+ B- AB+ AB-
37 6 34 6 10 2 4 1

.4
.34
.6
.45

.4
Solve the problem.

At the local racetrack, the favorite in a race has odds 3:2 in favor of winning. What is the probability that the favorite wins the race?

0.8
0.2
0.6
0.4

.6
Solve the problem.

Classify the events as dependent or independent. Events A and B where
P(A) = 0.8, P(B) = 0.1, and P(A and B) = 0.07

dependent
independent

dependent
Solve the problem.

A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an ace or a king.

4/13
2/13
8/13
1/13

2/13
Solve the problem.

The access code to a house’s security system consists of five digits. How many different codes are available if each digit can be repeated?

3125
5
100,000
32

100,000
Solve the problem.

Seven guests are invited for dinner. How many ways can they be seated at a dinner table if the table is straight with seats only on one side?

40,320
720
4
5040

5040
Solve the problem.

If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing a red card?

1/2
1/13
1/52
1/4

1/2
Solve the problem.

The distribution of Master’s degrees conferred by a university is listed in the table.

Major Frequency
Mathematics 216
English 207
Engineering 86
Business 176
Education 204

What is the probability that a randomly selected student graduating with a Master’s degree has a major of Education? Round your answer to three decimal places.

0.298
0.771
0.005
0.229

0.229
Solve the problem.

A group of students were asked if they carry a credit card. The responses are listed in the table.

class cc carrier no cc
Freshman 19 41
Sophomore 40 0

If a student is selected at random, find the probability that he or she is a freshman given that the student owns a credit card. Round your answers to three decimal places.

0.322
0.678
0.190
0.317

0.322
Solve the problem.

A group of students were asked if they carry a credit card. The responses are listed in the table

class has cc no cc
freshman 11 49
sophomore 27 13

0.289
0.270
0.711
0.980

0.711
Solve the problem.

Use Bayes’ theorem to solve this problem. A storeowner purchases stereos from two companies. From Company A, 550 stereos are purchased and 1% are found to be defective. From Company B, 850 stereos are purchased and 6% are found to be defective. Given that a stereo is defective, find the probability that it came from Company A.

66/113
11/113
102/113
17/113

11/113
Solve the problem.

Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn from a standard deck of 52 playing cards.
A: The result is a 7.
B: The result is a jack.

mutually exclusive
not mutually exclusive

mutually exclusive
Solve the problem.

Given that P(A or B)=1/6, P(A)=1/7, and P(A and B)=1/8, find P(B)

73/168
1/16
31/168
25/168

25/168
Solve the problem.

The distribution of Master’s degrees conferred by a university is listed in the table.
(assume that a student majors in only one subject)

Major Frequency
Mathematics 230
English 206
Engineering 86
Business 176
Education 222

What is the probability that a randomly selected student with a Master’s degree majored in English or Mathematics? Round your answer to three decimal places.

0.224
0.474
0.526
0.250

0.474
Solve the problem.

If a couple has seven boys and eight girls, how many gender sequences are possible?

16
15
6435
8

6435
Solve the problem.

A delivery route must include stops at three cities. If the route is randomly selected, find the probability that the cities will be arranged in alphabetical order. Round your answer to three decimal places.

0.03703704
0.16666667
0.33333333
0.125

0.16666667
Solve the problem.

The table lists the smoking habits of a group of college students.

no yes Heavy
man 135 52 5
woman 187 21 5

If a student is chosen at random, find the probability of getting someone who is a man or a non-smoker. Round your answer to three decimal places.

0.941
0.820
0.948
0.936

0.936
Solve the problem.

The distribution of Master’s degrees conferred by a university is listed in the table.
(assume that a student majors in only one subject)

Major Frequency
Mathematics 216
English 207
Engineering 85
Business 175
Education 215

What is the probability that a randomly selected student with a Master’s degree majored in Business, Education or Engineering? Round your answer to three decimal places.

0.334
0.290
0.529
0.471

0.529
Solve the problem.

How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if C must sit to the right of but not necessarily next to B?

48
20
60
24

60
Solve the problem.

How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if A and B must sit together?

120
48
12
24

48
Solve the problem.

The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many different ways can a representative visit five of these to investigate this week?

45
362,880
15,120
5

15,120
Solve the problem.

Classify the events as dependent or independent. Event A: A red candy is selected from a package with 30 colored candies and eaten. Event B: A blue candy is selected from the same package and eaten.

dependent
independent

dependent
Solve the problem.

Decide if the events A and B are mutually exclusive or not mutually exclusive, A die is rolled.
A: The result is a 3.
B: The result is an odd number.

not mutually exclusive
mutually exclusive

not mutually exclusive
Solve the problem.

A group of students were asked if they carry a credit card. The responses are listed in the table.

class cc carrier no cc
Freshman 13 47
Sophomore 22 18

If a student is selected at random, find the probability that he or she owns a credit card given that the student is a sophomore. Round your answer to three decimal places.

0.550
0.450
0.220
0.629

0.550
Solve the problem.

If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing an ace?

1/2
1/4
1/52
1/13

1/13
Solve the problem.

Classify the statement as an example of classical probability, empirical probability, or subjective probability. In California’s Pick Three lottery, a person selects a 3-digit number. The probability of winning California’s Pick Three lottery is 1/1000

empirical probability
classical probability
subjective probability

classical probability
Solve the problem.

A study of 1000 randomly selected flights of a major airline showed that 782 of the flights arrived on time. What is the probability of a flight arriving on time?

500/109
391/500
109/500
500/391

391/500
Solve the problem.

The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.1, what is P(A and B)?

0.5
0.3
0
0.02

Solve the problem.

The table lists the smoking habits of a group of college students.

no yes Heavy
man 135 41 5
woman 187 21 5

If a student is chosen at random, find the probability of getting someone who is a man or a woman. Round your answer to three decimal places.

0.918
0.197
0.803
1

1
Solve the problem.

Use Bayes’ theorem to solve this problem. A storeowner purchases stereos from two companies. From Company A, 600 stereos are purchased and 11% are found to be defective. From Company B, 350 stereos are purchased and 1% are found to be defective. Given that a stereo is defective, find the probability that it came from Company A.

77/139
132/139
7/139
12/139

132/139
Solve the problem.

Find the area under the standard normal curve to the left of z = 1.5

0.1599
0.7612
0.9332
0.0668

0.9332
Solve the problem.

Use the standard normal distribution to find P(0 < z < 2.25). 0.5122 0.7888 0.4878 0.8817

0.4878
Solve the problem.

Find the area of the indicated region under the standard normal curve.

0.309
0.6562
1.309
0.3438

0.6562
Solve the problem.

The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting less than 250 days.

0.1151
0.0066
0.1591
0.0606

0.1151
Solve the problem.

Find the z-scores for which 98% of the distribution’s area lies between -z and z.

(-0.99,0.99)
(-1.96, 1.96)
(-1.645, 1.645)
(-2.33, 2.33)

(-2.33, 2.33)
Solve the problem.

Use a standard normal table to find the z-score that corresponds to the cumulative area of 0.01.

-0.255
0.255
-2.33
2.33

-2.33
Solve the problem.

Two high school students took equivalent language tests, one in German and one in French. The student taking the German test, for which the mean was 66 and the standard deviation was 8, scored an 82, while the student taking the French test, for which the mean was 27 and the standard deviation was 5, scored a 35. Compare the scores.

a)A score of 82 with a mean of 66 and a standard deviation of 8 is better.
b)The two scores are statistically the same.
c)You cannot determine which score is better from the given information.
d)A score of 35 with a mean of 27 and a standard deviation of 5 is better.

a)A score of 82 with a mean of 66 and a standard deviation of 8 is better.
Solve the problem.

The lengths of pregnancies are normally distributed with a mean of 264 days and a standard deviation of 15 days. If 36 women are randomly selected, find the probability that they have a mean pregnancy between 264 days and 266 days.

0.5517
0.7881
0.2881
0.2119

0.2881
Solve the problem.

Find the area under the standard normal curve to the right of z = -1.25.

0.7193
0.6978
0.5843
0.8944

0.8944
Solve the problem.

An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with mean = 15.5 and standard deviation= 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases?

0.1056
0.3944
0.8944
0.4040

0.8944
Solve the problem.

Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find the percentage of men meeting these height requirements.

31.12%
96.26%
99.93%
3.67%

96.26%
Solve the problem.

Find the z-score for which 99% of the distribution’s area lies between -z and z.

(-1.645, 1.645)
(-2.575, 2.575)
(-1.96, 1.96)
(-1.28, 1.28)

(-2.575, 2.575)
Solve the problem.

Assume that the heights of men are normally distributed with a mean of 67.9 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height greater than 68.9 inches.

0.8188
0.0021
9.9671
0.9005

0.0021
Solve the problem.

Assume that blood pressure readings are normally distributed with a mean of 116 and a standard deviation of 4.8. If 36 people are randomly selected, find the probability that their mean blood pressure will be less than 118.

0.8615
0.9938
0.0062
0.8819

0.9938
Solve the problem.

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be less than 12.1 ounces.

0.3216
0.0668
0.9332
0.2123

0.9332
Solve the problem.

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be greater than 12.1 ounces.

0.9332
0.2123
0.0668
0.3216

0.0668
Solve the problem.

Compare the scores: a score of 220 on a test with a mean of 200 and a standard deviation of 21 and a score of 90 on a test with a mean of 80 and a standard deviation of 8.

a) A score of 220 with a mean of 200 and a standard deviation of 21 is better.
b) The two scores are statistically the same.
c) A score of 90 with a mean of 80 and a standard deviation of 8 is better.
d) You cannot determine which score is better from the given information.

c) A score of 90 with a mean of 80 and a standard deviation of 8 is better.
Solve the problem.

Find the area under the standard normal curve between z = 0 and z = 3.

0.4641
0.9987
0.0010
0.4987

0.4987
Find the area under the standard normal curve to the left of z = 1.25.

0.7682
0.8944
0.1056
0.2318

0.8944
Solve the problem.

Find the area under the standard normal curve to the right of z = -1.25.

0.7193
0.6978
0.5843
0.8944

0.8944
Solve the problem.

Use the standard normal distribution to find P(0 < z < 2.25). 0.5122 0.7888 0.4878 0.8817

0.4878
Solve the problem.

Find the area of the indicated region under the standard normal curve.

0.0968
0.0823
0.9032
0.9177

0.9032
Solve the problem.

IQ test scores are normally distributed with a mean of 99 and a standard deviation of 11. An individual’s IQ score is found to be 109. Find the z-score corresponding to this value.

-1.10
0.91
-0.91
1.10

0.91
Solve the problem.

The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. A baby is premature if it is born three weeks early. What percentage of babies are born prematurely?

6.81%
8.08%
10.31%
9.21%

8.08%
Solve the problem.

The distribution of cholesterol levels in teenage boys is approximately normal with mean= 170 and standard deviation= 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 200.

0.3419
0.1587
0.8413
0.2138

0.1587
An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with mean= 15.5 and standard deviation= 3.6. What is the probability that during a given week the airline will lose between 10 and 20 suitcases?

0.1056
0.8314
0.4040
0.3944

0.8314
Solve the problem.

Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find the percentage of men meeting these height requirements.

31.12%
96.26%
99.93%
3.67%

96.26%
Solve the problem.

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of -1.645.

82.3
75.3
91.0
79.1

75.3
Solve the problem.

Use a standard normal table to find the z-score that corresponds to the cumulative area of 0.01.

-0.255
0.255
-2.33
2.33

-2.33
Solve the problem.

A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 47,500 miles and a standard deviation of 3000 miles. If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty?

51,340
52,435
42,565
43,660

43,660
Solve the problem.

Based on previous clients, a marriage counselor concludes that the majority of marriages that begin with cohabitation before marriage will result in divorce. Does this statement describe inferential statistics or descriptive statistics?

inferential statistics
descriptive statistics

inferential statistics
Solve the problem.

From past figures, it is predicted that 43% of the registered voters in California will vote in the June primary. Does this statement describe:

descriptive statistics?
inferential statistics?

inferential statistics?
Solve the problem.

Classify the number of seats in a movie theater as qualitative data or quantitative data.

qualitative data
quantitative data

quantitative data
Solve the problem.

Identify the level of measurement for data that are a list of 1247 social security numbers.

ratio
ordinal
nominal
interval

nominal
Solve the problem.

Identify the level of measurement for data that are the numbers on the shirts of a girl’s soccer team.

ratio
ordinal
nominal
interval

ordinal
Solve the problem.

What method of data collection would you use to collect data for a study where a drug was given to 57 patients and a placebo to another group of 57 patients to determine if the drug has an effect on a patient’s illness?

use sampling
use a simulation
take a census
perform an experiment

perform an experiment
Solve the problem.

A researcher for an airline interviews all of the passengers on five randomly selected flights. What sampling technique is used?

systematic
random
convenience
stratified
cluster

cluster
Solve the problem.

At a local community college, five statistics classes are randomly selected and all of the students from each class are interviewed. What sampling technique is used?

systematic
random
convenience
stratified
cluster

cluster
Solve the problem.

Thirty-five sophomores, 35 juniors and 49 seniors are randomly selected from 230 sophomores, 280 juniors and 577 seniors at a certain high school. What sampling technique is used?

random
systematic
stratified
convenience
cluster

stratified
For the dot plot below, what is the maximum and what is the minimum entry?

max: 14; min: 12
max: 54; min: 12
max: 54; min: 15
max: 17; min: 12

max: 17; min: 12
Solve the problem.

Use the ogive below to approximate the number in the sample.

28
100
80
341

80
Solve the problem.

A sample of candies have weights that vary from 2.35 grams to 4.75 grams. Use this information to find the upper and lower limits of the first class if you wish to construct a frequency distribution with 12 classes.

2.35- 2.75
2.35- 2.65
2.35- 2.54
2.35- 2.55

2.35- 2.54
Solve the problem.

A city in the Pacific Northwest recorded its highest temperature at 74 degrees Fahrenheit and its lowest temperature at 23 degrees Fahrenheit for a particular year. Use this information to find the upper and lower limits of the first class if you wish to construct a frequency distribution with 10 classes.

23-27
18-28
23-28
23-29

23- 27
Solve the problem.

Identify the class width used in the frequency distribution.

Miles (per day) Frequency
1 – 6 28
7 – 12 21
13 – 18 8
19 – 24 11

7
6
5
12

6
Solve the problem.

Identify the midpoint of the first class.

Weight (in Pounds) Frequ.
135-139 6
140-144 4
145-149 11
150-154 15
155-160 8

137
139
135
11

137
Solve the problem.

Identify the midpoint of the first class.

Height (in inches) Frequency
50-52 5
53-55 8
56-58 12
59-61 13
62-64 11

52
50
51
49.5

51
Solve the problem.

The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the mode speed.
181.1 202.2 190.1 201.4 191.3 201.4 192.2 201.2 193.2 201.2 194.5 199.2 196.0 196.2

bimodal
201.2
no mode
201.4

bimodal
Solve the problem.

The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the median speed.

181.1 202.2 190.1 201.4 191.3 201.4 192.2 201.2 193.2 201.2 194.5 199.2 196.0 196.2

201.2
196.1
196.7
192.2

196.1
Solve the problem.

For the following data, approximate the mean number of phone calls per day.

phone calls (per day) Freque.
8-11 48
12-15 16
16-19 42
20-23 34
24-27 45

16
37
19
17
18

18
Solve the problem.

The heights (in inches) of 10 adult males are listed below. Find the sample standard deviation.

70 72 71 70 69 73 69 68 70 71

1.49
2.38
3
70

1.49
Solve the problem.

The grade point averages for 10 students are listed below. Find the range of the data.

2.0 3.2 1.8 2.9 .9 4.0 3.3 2.9 3.6 .8

2.8
1.4
2.45
3.2

3.2
Solve the problem.

Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = O. Grades are weighted according to credit hours. If a student receives an A in a four-unit class, a D in a two-unit class, a B in a three-unit class and a C in a three-unit class, what is the student’s grade point average?

2.75
2.50
3.00
1.75

2.75
Solve the problem.

Find the z-score for the value 88, when the mean is 95 and the standard deviation is 7.

z = -1.14
z = -1.00
z = 0.85
z = -0.85

z = -1.00
Solve the problem.

The average IQ of students in a particular calculus class is 110, with a standard deviation of 5. The distribution is roughly bell-shaped. Use the Empirical Rule to find the percentage of students with an IQ above 120.

15.85%
2.5%
13.5%
11.15%

2.5%
Solve the problem.

The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find Q1.

154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265

171
180
184.5
200

180
Solve the problem.

The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be considered unusual.

1200g
2000g
3600g
2353g

3600 g
Solve the problem.

How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if A and B must sit together?

24
48
120
12

48
Solve the problem.

If a couple plans to have five children, how many gender sequences are possible?

5
32
25
3125

32
Solve the problem.

A single six-sided die is rolled. Find the probability of rolling a number less than 3.

0.25
0.333
0.5
0.1

0.333
Solve the problem.

Classify the events as dependent or independent.
The events of getting two aces when two cards are drawn from a deck of playing cards and the first card is replaced before the second card is drawn.

independent
dependent

independent
Solve the problem.

Decide if the events A and B are mutually exclusive or not mutually exclusive. A student is selected at random.
A: The student is taking a math course.
B: The student is a business major.

not mutually exclusive
mutually exclusive

not mutually exclusive
Solve the problem.

A group of students were asked if they carry a credit card. The responses are listed in the table.

has cc no cc
13 47
22 18

If a student is selected at random, find the probability that he or she owns a credit card given that the student is a sophomore. Round your answer to three decimal places.

0.629
0.450
0.550
0.220

0.550
Solve the problem.

Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a newborn baby is a boy is 1/2.

empirical probability
classical probability
subjective probability

classical probability
Solve the problem.

A study of 1000 randomly selected flights of a major airline showed that 782 of the flights arrived on time. What is the probability of a flight arriving on time?

391/500
500/391
109/500
500/109

391/500
Solve the problem.

The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.1, what is P(A and B)?

0.3
0.02
0
0.5

Solve the problem.

The distribution of Master’s degrees conferred by a university is listed in the table.
(assume that a student majors in only one subject)

major Frequency
mathematics 216
English 207
Engineering 79
Business 179
Education 226

What is the probability that a randomly selected student with a Master’s degree majored in Business, Education or Engineering? Round your answer to three decimal places.

0.532
0.282
0.468
0.337

0.532
Solve the problem.

The chances of winning the California Lottery are one chance in twenty-two million. Does this statement describe:

inferential statistics?
Descriptive statistics?

inferential statistics?
Solve the problem.

Identify the level of measurement for data that are the temperature of 90 refrigerators.

nominal
interval
ordinal
ratio

interval
Solve the problem.

A market researcher randomly selects 200 drivers under 35 years of age and 100 drivers over 35 years of age. What sampling technique was used?

random
stratified
systematic
cluster
convenience

stratified
Solve the problem.

Classify the statement as an example of classical probability, empirical probability, or subjective probability. In California’s Pick Three lottery, a person selects a 3-digit number. The probability of winning California’s Pick Three lottery is 1/1000.

empirical probability
classical probability
subjective probability

classical probability
Solve the problem.

For the following data, approximate the mean miles per day.

Miles (per day) Frequency
1-2 23
3-4 16
5-6 26
7-8 30
9-10 29

6
5
25
7

6
Solve the problem.

For the following data set, approximate the sample standard deviation.

Height (in inches) Frequency
50-52 5
53-55 8
56-58 12
59-61 13
62-64 11

2.57
.98
1.86
3.85

3.85
Solve the problem.

Lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 16 days. Use the Empirical Rule to determine the percentage of women whose pregnancies are between 252 and 284 days.

50%
68%
95%
99.7%

68%
Solve the problem.

Seven guests are invited for dinner. How many ways can they be seated at a dinner table if the table is straight with seats only on one side?

4
720
40,320
5040

5040
Solve the problem.

A coin is tossed. Find the probability that the result is heads.

0.9
1
0.5
0.1

0.5
Solve the problem.

Decide if the events A and B are mutually exclusive or not mutually exclusive. A die is rolled.
A: The result is an odd number.
B: The result is an even number.

mutually exclusive
not mutually exclusive

mutually exclusive
Solve the problem.

A group of students were asked if they carry a credit card. The responses are listed in the table.

has cc no cc
24 36
37 3

If a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places.

0.400
0.240
0.600
0.393

0.400
Solve the problem.

If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing a red card?

1/2
1/52
1/4
1/13

1/2
Solve the problem.

If a couple has nine boys and two girls, how many gender sequences are possible?

11
55
16
8

55
Solve the problem.

Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a train will be in an accident on a specific route is 1%.

classical probability
empirical probability
subjective probability

Solve the problem.

Determine the margin of error if the grade point averages for 10 randomly selected students from a class of 125 students has a mean of = 2.7. Assume the grade point average of the 125 students has a mean of = 2.9.

0.2
2.6
-0.2
2.8

0.2
Solve the problem.

A random sample of 40 students has a test score average with a standard deviation of 11.7. Find the margin of error if c = 0.98.

1.81
1.85
4.31
0.68

4.31
Solve the problem.

A random sample of 40 students has a test score with average = 81.5 and s = 10.2. Construct the confidence interval for the (mean symbol) population mean, if c = 0.90.

(66.3, 89.1)
(78.8, 84.2)
(51.8, 92.3)
(71.8, 93.5)

(78.8, 84.2)
Solve the problem.

Find the critical value, tc for c = 0.99 and n = 10.

2.2821
2.262
1.833
3.250

3.250
Solve the problem.

Find the value of E, the margin of error, for c = 0.90, n = 10 and s = 3.6.

2.06
2.09
0.66
1.57

2.09
Solve the problem.

For a sample of 20 IQ scores the mean score is 105.8. The standard deviation, , is 15. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval.

Use a t-distribution

Use a normal distribution

Neither a normal distribution nor a t-distribution can be used.

Use a normal distribution.
Solve the problem.

Construct a 95% confidence interval for the population mean, . Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2.

(87.12, 98.32)
(77.29, 85.71)
(66.35, 69.89)
(56.12, 78.34)

(77.29, 85.71)
Solve the problem.

A survey of 100 fatal accidents showed that 13 were alcohol related. Find a point estimate for p, the population proportion of accidents that were alcohol related.

0.87
0.149
0.13
0.115

0.13
Solve the problem.

In a survey of 2480 golfers, 15% said they were left-handed. The survey’s margin of error was 3%. Find the confidence interval for p.

84.5%
98.5%
95%
80%

84.5%
Solve the problem.

A random sample of 150 students has a grade point average with a standard deviation of 0.78. Find the margin of error if c = 0.98.

0.12
0.08
0.11
0.15

0.15
Solve the problem.

A group of 49 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8. Construct a 98% confidence interval for the population mean.

(20.3, 24.5)
(21.1, 23.7)
(19.8, 25.1)
(18.8, 26.3)

(21.1, 23.7)
Solve the problem.

In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6 with a standard deviation of 5.8 hours. Find the 98% confidence interval for the population mean.

(19.1, 20.4)
(17.5, 21.7)
(18.3, 20.9)
(14.1, 23.2)

(17.5, 21.7)
Solve the problem.

Construct a 95% confidence interval for the population mean, . Assume the population has a normal distribution. A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours.

(321.7, 365.8)
(628.5, 661.5)
(531.2, 612.9)
(876.2, 981.5)

(628.5, 661.5)
Solve the problem.

Construct a 98% confidence interval for the population mean, . Assume the population has a normal distribution. A study of 14 bowlers showed that their average score was 192 with a standard deviation of 8.

(186.3, 197.7)
(328.3, 386.9)
(115.4, 158.8)
(222.3, 256.1)

(186.3, 197.7)
Solve the problem.

A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed.

3.60 4.50 2.8 6.3 2.6 5.2 6.75 4.25 8 3

Find the 95% confidence interval for the true mean.

($1.35, $2.85)
($2.11, $5.34)
($3.39, $6.01)
($4.81, $6.31)

($3.39, $6.01)
Solve the problem.

A local bank needs information concerning the checking account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 98% confidence interval for the true mean. Assume that the account balances are normally distributed.

($513.17, $860.33)
($238.23, $326.41)
($487.31, $563.80)
($326.21, $437.90)

($513.17, $860.33)
Solve the problem.

A survey of 250 homeless persons showed that 86 were veterans. Find a point estimate p, for the population proportion of homeless persons who are veterans.

0.34400002
0.524
0.256
0.65599998

0.34400002
Solve the problem.

A survey of 2650 golfers showed that 392 of them are left-handed. Find a point estimate for p, the population proportion of golfers that are left-handed.

0.129
0.174
0.852
0.148

0.148
Given H0: U ≤ 25 and Ha: μ > 25, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

left-tailed
right-tailed
two-tailed

right-tailed
Solve the problem.

The mean age of bus drivers in Chicago is 56.9 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

There is not sufficient evidence to reject the claim = 56.9.

There is sufficient evidence to support the claim = 56.9.

There is not sufficient evidence to support the claim = 56.9.

There is sufficient evidence to reject the claim = 56.9.

There is not sufficient evidence to reject the claim = 56.9.
Solve the problem.

Given H0: p = 0.85 and α = 0.10, which level of confidence should you use to test the claim?

80%
95%
99%
90%

90%
Solve the problem.

Find the critical value for a two-tailed test with α = 0.01 and n = 30.

±1.96
±2.575
±2.33
±1.645

±2.575
you wish to test the claim that μ > 6 at a level of significance of α = 0.05 and are given sample statistics n = 50, x = 6.3, and s = 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal places.

2.31
1.77
3.11
0.98

1.77
Solve the problem.

Suppose you want to test the claim that μ < 65.4. Given a sample size of n = 35 and a level of significance of α = 0.01 when should you reject H0? Reject H0 if the standardized test is less than -2.575. Reject H0 if the standardized test statistic is less than -1.96. Reject H0 if the standardized test statistic is less than -1.28. Reject H0 if the standardized test statistic is less than -1.645.

Reject H0 if the standardized test statistic is less than -1.28.
Suppose you are using α =0.05 to test the claim that μ ≠ 34 using a P-value. You are given the sample statistic n= 35 33.1, and s = 2.7. Find the P-value.

0.0244
0.1003
0.0448
0.0591

0.0448
Solve the problem.

Given H0: μ = 25, Ha: μ ≠ 25, and P = 0.028. Do you reject or fail to reject H0 at the 0.01 level of significance?

reject H0

fail to reject H0

not sufficient information to decide

fail to reject H0
Find the standardized test statistic t for a sample with n = 12, x = 18.2000, s = 2.2, and α = 0.01 if H0: μ = 17. Round your answer to three decimal places.

1.890
2.001
1.991
2.132

1.890
Solve the problem.

Find the standardized test statistic t for a sample with n = 15, x = 5.4000001, s = 0.8, and α = 0.05 if H0: μ ≤ 5.0999999. Round your answer to three decimal places.

1.728
1.452
1.631
1.312

1.452
Solve the problem.

A car maker claims that its new sub-compact car gets better than 52 miles per gallon on the highway. Determine whether the hypothesis test for this is left-tailed, right-tailed, or two-tailed.

left-tailed
two-tailed
right-tailed

right-tailed
Solve the problem.

The mean age of bus drivers in Chicago is greater than 56.2 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

There is sufficient evidence to support the claim μ > 56.2.

There is not sufficient evidence to reject the claim μ > 56.2.

There is sufficient evidence to reject the claim μ > 56.2.

There is not sufficient evidence to support the claim μ > 56.2.

There is not sufficient evidence to support the claim > 56.2.
Solve the problem.

The mean IQ of statistics teachers is greater than 160. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

There is not sufficient evidence to support the claim μ > 160.

There is sufficient evidence to support the claim μ > 160.

There is not sufficient evidence to reject the claim μ > 160.

There is sufficient evidence to reject the claim μ > 160.

There is sufficient evidence to support the claim μ > 160.
Solve the problem.

The mean score for all NBA games during a particular season was less than 91 points per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

There is sufficient evidence to reject the claim μ < 91. There is sufficient evidence to support the claim μ < 91. There is not sufficient evidence to reject the claim μ < 91. There is not sufficient evidence to support the claim μ < 91

There is not sufficient evidence to support the claim μ < 91
You wish to test the claim that μ = 940 at a level of significance of α = 0.01 and are given sample statistics n = 35, x = 910 and s = 82. Compute the value of the standardized test statistic. Round your answer to two decimal places.

-3.82
-2.16
-5.18
-4.67

-2.16
suppose you are using α = 0.01 to test the claim that μ ≤ 29 using a P-value. You are given the sample statistics n = 40, x = 30.8, and s = 4.3. Find the P-value.

0.1030
0.0211
0.0040
0.9960

0.0040
Solve the problem.

Find the standardized test statistic t for a sample with n = 25, x = 21, s = 3, and α = 0.005 if Ha: μ > 20. Round your answer to three decimal places.

1.997
1.239
1.667
1.452

1.667
Solve the problem.

Determine the standardized test statistic, z, to test the claim about the population proportion p = 0.250 given n=48 and p = 0.231. Use α = 0.01.

-1.18
-0.304
-2.87
-0.23

-0.304
Solve the problem.

A researcher claims that 73% of voters favor gun control. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.

right-tailed
left-tailed
two-tailed

two-tailed
Solve the problem.

An elementary school claims that the standard deviation in reading scores of its fourth grade students is less than 3.45. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.

right-tailed
two-tailed
left-tailed

left-tailed
Solve the problem.

The mean age of bus drivers in Chicago is 47.4 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

There is sufficient evidence to support the claim μ = 47.4.

There is not sufficient evidence to reject the claim μ = 47.4.

There is not sufficient evidence to support the claim μ = 47.4.

There is sufficient evidence to reject the claim μ = 47.4.

There is sufficient evidence to reject the claim μ = 47.4.
Solve the problem.

The mean age of bus drivers in Chicago is greater than 56.2 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

There is sufficient evidence to support the claim μ > 56.2.

There is not sufficient evidence to reject the claim μ > 56.2.

There is sufficient evidence to reject the claim μ > 56.2.

There is not sufficient evidence to support the claim μ > 56.2.

There is not sufficient evidence to support the claim μ > 56.2.
Solve the problem.

The mean score for all NBA games during a particular season was less than 91 points per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

There is sufficient evidence to reject the claim μ < 91. There is sufficient evidence to support the claim μ < 91. There is not sufficient evidence to reject the claim μ < 91. There is not sufficient evidence to support the claim μ < 91.

Solve the problem.

The mean IQ of statistics teachers is greater than 130. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

There is sufficient evidence to reject the claim μ > 130.

There is not sufficient evidence to support the claim μ > 130.

There is not sufficient evidence to reject the claim μ > 130.

There is sufficient evidence to support the claim μ > 130.

There is not sufficient evidence to support the claim μ > 130.
Solve the problem.

Given H0: μ ≤12, for which confidence interval should you reject H0?

(11.5, 12.5)
(13, 16)
(10, 13)

Solve the problem.

Given H0: p = 0.85 and α = 0.10, which level of confidence should you use to test the claim?

80%
95%
99%
90%

Solve the problem.

Find the critical value for a left-tailed test with α = 0.025 and n = 50.

-2.575
-1.96
-1.645
-2.33

-1.96
Solve the problem.

Suppose you want to test the claim that μ ≠ 3.5. Given a sample size of n = 33 and a level of significance of α = 0.05 when should you reject H0 ?

Reject H0 if the standardized test statistic is greater than 2.33 or less than -2.33

Reject H0 if the standardized test statistic is greater than 2.575 or less than -2.575.

Reject H0 if the standardized test statistic is greater than 1.96 or less than -1.96.

Reject H0 if the standardized test statistic is greater than 1.645 or less than -1.645

Reject H0 if the standardized test statistic is greater than 1.96 or less than -1.96
Solve the problem.

Suppose you are using α = 0.01 to test the claim that μ ≤ 29 using a P-value. You are given the sample statistics n = 40, x = 30.8, and s = 4.3. Find the P-value.

0.1030
0.0211
0.0040
0.9960

±
Solve the problem.

Given H0: μ = 25, Ha: μ ≠ 25, and P = 0.028. Do you reject or fail to reject H0 at the 0.01 level of significance?

reject H0

fail to reject H0

not sufficient information to decide

fail to reject H0
Solve the problem.

Given H0: µ ≥18and P = 0.085. Do you reject or fail to reject H0 at the 0.05 level of significance?

reject H0

fail to reject H0

not sufficient information to decide

fail to reject H0
Solve the problem.

You wish to test the claim that μ > 23 at a level of significance of α = 0.05 and are given sample statistics n = 50, x = 23.3000002, and s = 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal places.

3.11
0.98
2.31
1.77

1.77
Solve the problem.
You wish to test the claim that μ > 6 at a level of significance of α = 0.05 and are given sample statistics n = 50, x = 6.3, and s = 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal places.

2.31
1.77
3.11
0.98

1.77
Solve the problem.

Calculate the correlation coefficient, r, for the data below.

x -9 -7 0 -3 -5 -6 -4 -2 -1 -8
y -2 0 17 9 6 2 7 11 14 0

0.990
0.819
0.792
0.881

0.990
Solve the problem.

Calculate the correlation coefficient, r, for the data below.

x:-12 -10 -3 -6 -8-9 -7 -5-4 -11
Y:14 -3 11 0 1 4 8 -2 9 10

-0.104
-0.549
-0.581
-0.132

-0.104
Solve the problem.

Given a sample with r = 0.321, n = 30, and α = 0.10, determine the standardized test statistic t necessary to test the claim ρ = 0. Round answers to three decimal places.

1.793
2.561
3.198
2.354

1.793
Solve the problem.

Given a sample with r = 0.321, n = 30, and = 0.10, determine the critical values t0 necessary to test the claim Ε = 0.

± 1.311
± 0.683
± 1.701
± 2.462

±1.701
Solve the problem.

Find the equation of the regression line for the given data.

x: -5 -3 4 1 -1 -2 0 2 3 -4
y: 11 6 -6 -1 3 4 1 -4 -5 8

y= -1.885x + 0.758
y= -0.758x – 1.885
y= 0.758x + 1.885
y= 1.885x – 0.758

y= -1.885x + 0.758
Given the equation of a regression line is y = 5x – 6, what is the best predicted value for y given x = 10? Assume that the variables x and y have a significant correlation.

44
55
9
56

44
Solve the problem.

Use the regression equation to predict the value of y for x = 3.2. Assume that the variables x and y have a significant correlation.

x: -5 -3 4 1 -1 -2 0 2 3 -4
y: 11 6 -6 -1 3 4 1 -4 -5 8

-5.274
0.541
6.790
4.311

-5.274
Find the standard error of estimate, se, for the data below, given that y = -1.885x + 0.758.

x: -5 -3 4 1 -1 -2 0 2 3 -4
y: 11 6 -6 -2 3 4 1 -4 -5 8

0.613
0.011
0.312
0.981

0.613
Solve the problem.

Construct a 95% prediction interval for y given x = -3.5, = 2.097x – 0.552 and se = 0.976.

x: -5 -3 4 1-1 -2 0 2 3-4
Y: -10 -8 9 1 -2 -6 -1 3 6 -8

-3.187 < y < -2.154 -10.367 < y < -5.417 -4.598 < y < -1.986 -12.142 < y < -6.475

-10.367 < y < -5.417
Solve the problem.

A researcher found a significant relationship between a person’s age, x1, the number of hours a person works per week, x2, and the number of accidents, y, the person has per year. The relationship can be represented by the multiple regression equation y = -3.2 + 0.012×1 + 0.23×2. Predict the number of accidents per year (to the nearest whole number) for a person whose age is 37 and who works 54 hours per week.

10
11
9
12

10
Solve the problem.

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Calculate the correlation coefficient, r.

temp x: 74 87 93 92 90 100 77 102 82
# of absences y: 5 9 12 12 10 17 6 17 7

0.881
0.819
0.980
0.890

.0980
Solve the problem.

The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. Calculate the correlation coefficient, r.

Age x: 4144 48 51 54 56 60 64 68
Pressure, y: 111 115 118 126 137 140 143 145 147.

0.908
0.890
0.960
0.998

0.960
Solve the problem.

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager’s sales representatives travel per month and the amount of sales (in thousands of dollars) per month. Calculate the correlation coefficient, r.

Miles traveled x 5 6 13 10 11 18 6 4 14
Sales y: 41 43 88 72 75 71 58 65 130

0.561
0.791
0.632
0.717

0.632
Solve the problem.

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Find the equation of the regression line for the given data.

# of absences x: 0 3 6 4 9 2 15 8 5
Final grade: 98 86 80 4 82 7192 55 76 82

y= 96.14x – 2.75
y= -96.14x + 2.75
y= -2.75x + 96.14
y= -2.75x – 96.14

y= -2.75x + 96.14
Solve the problem.

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. What is the best predicted value for y given x = 95 Assume that the variables x and y have a significant correlation.

Temp x: 72 85 91 90 88 98 75 100 80
# of absences y: 3 7 10 10 8 15 4 15 5

15
13
12
14

12
Solve the problem.

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. What is the best predicted value for y given x = 7? Assume that the variables x and y have a significant correlation.

# of absences x: 0 3 6 4 9 2 15 8 5
Final Grade y: 98 86 80 82 71 92

76
78
79
77

77
Solve the problem.

The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. Find the standard error of estimate, se, given that

age x: 38 41 45 48 51 53 57 61 65
pressure y: 116 120 123 131 142 145 148 150 152

5.572
3.099
6.981
4.199

4.199
Solve the problem.

A researcher found a significant relationship between a person’s age, x1, the number of hours a person works per week, x2, and the number of accidents, y, the person has per year. The relationship can be represented by the multiple regression equation y = -3.2 + 0.012×1 + 0.23×2. Predict the number of accidents per year (to the nearest whole number) for a person whose age is 41 and who works 31 hours per week.

5
6
4
3

4
Solve the problem.

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Calculate the correlation coefficient r.

hrs x: 5 7 4 10 4 6 6 7 8 5
Scores y: 66 81 61 89 67 79 86 91 91 5

0.654
0.761
0.847
0.991

0.847
Solve the problem.

Calculate the correlation coefficient, r, for the data below.

x: -10 -8 -1 -4 -6 -7 -5 -3 -2 -9
y: 2 -3 -15 -10

-0.885
-0.778
-0.995
-0.671

-0.995
Solve the problem.

Given a sample with r = -0.541, n = 20, and α = 0.01, determine the standardized test statistic t necessary to test the claim Ε = 0. Round answers to three decimal places.

-5.132

-3.251

-4.671

-2.729

-2.729
Solve the problem.

Given a sample with r = -0.765, n = 22, and α = 0.02, determine the critical values t0 necessary to test the claim E = 0.

± 2.080
± 2.831
± 2.528
± 1.721

± 2.528
Solve the problem.

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the equation of the regression line for the given data.

hrs x: 3 5 2 8 2 4 4 5 6
Scores Y: 65 80 60 88 66 78 85 90 90 71

y= -56.11x – 5.044
y= 56.11x – 5.044
y= 5.044x + 56.11
y= -5.044x + 56.11

y= 5.044x + 56.11
Solve the problem.

Use the regression equation to predict the value of y for x = 3.2. Assume that the variables x and y have a significant correlation.

x: -5 -3 4 1 -1 -2 0 2 3 -4
y: 11 6 -6 -1 3 4 1 -4 -5 8

-5.274
0.541
6.790
4.311

-5.274
Solve the problem.

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. What is the best predicted value for y given Assume that the variables x and y have a significant correlation.

Temp x: 72 85 91 90 88 98 75 100
# of absences y: 3 7 10 10 8 15 4 15

15
13
12
14

12
Solve the problem.

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. What is the best predicted value for y given Assume that the variables x and y have a significant correlation.

# of absences x: 0 3 6 4 9 2 15 8
Final grade y: 98 86 80 82 71 92 55 76

76
78
79
77

77
Solve the problem.

Find the standard error of estimate, se, for the data below, given that y = -2.5x

x: -1 -2 -3 -4
y: 2 6 7 10

0.532
0.349
0.675
0.866

0.866
Solve the problem.

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the standard error of estimate, se, given that y = 5.044x + 56.11.

hrs x: 3 5 2 8 2 4 4 5 6 3
scores y: 65 80 60 88 66 78 85 90 90 71

9.875
7.913
8.912
6.305

6.305
Solve the problem.

Construct a 95% prediction interval for y given x = -3.5, y = 2.097x – 0.552 and se = 0.976.

x: -5 -3 4 1 -1 -2 0 2 3 -4
y: -10 -8 9 1 -2 -6 -1 3 6 -8

-3.187 < y < -2.154 -10.367 < y < -5.417 -4.598 < y < -1.986 -12.142 < y < -6.475

-10.367 < y < -5.417
Solve the problem.

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Construct a 95% prediction interval for y, the number of days absent, given x = 95 degrees, y = 0.449x – 30.27 and se = 0.934.

tep x: 72 85 91 90 88 98 75 100 80
# of absences y: 3 7 10 10 8 15 4 15 5

4.321 < y < 6.913 3.176 < y < 5.341 9.957 < y < 14.813 6.345 < y < 8.912

9.957 < y < 14.813
Solve the problem.

A multiple regression equation is y = -35,000 + 130×1 + 20,000×2, where x1 is a person’s age, x2 is the person’s grade point average in college, and y is the person’s income. Predict the income for a person who is 26 years old and had a college grade point average of 2.3.

$485,299
$84,380
$49,380
$14,380

$14,380
Solve the problem.

A researcher found a significant relationship between a person’s age, x1, the number of hours a person works per week, x2, and the number of accidents, y, the person has per year. The relationship can be represented by the multiple regression equation y = -3.2 + 0.012×1 + 0.23×2. Predict the number of accidents per year (to the nearest whole number) for a person whose age is 41 and who works 31 hours per week.

5
6
4
3

4
Solve the problem.

Given the size of a human’s brain, x, and their score on an IQ test, y, would you expect a positive correlation, a negative correlation, or no correlation?

no correlation
negative correlation
positive correlation

no correlation