# Stat 200 Exam 2

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**Stat 200 Exam 2**

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0%| 1. The level of significance associated with a significance test is the probability A) of rejecting a true null hypothesis. B) of not rejecting a true null hypothesis. C) that the null hypothesis is true. D) that the alternative hypothesis is true. Feedback: This level of significance, commonly set to ? equal to 0. 05, is used to set the cut-off as the maximum probability a researcher would use in order to reject a true null hypothesis. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 2.

A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71. 8. A significance test is done and the p-value is 0. 02. What is the most appropriate conclusion based on ? of 0. 05? A) Conclude that the population average pulse rate is 70. B) Conclude that the population average pulse rate is 71. 8. C) Reject the hypothesis that the population average pulse rate is 70. D) Reject the hypothesis that the sample average pulse rate is 70. Feedback: Since the p-value is less than ? we would reject the Ho the null hypothesis that the population average pulse rate is 70.

Points Earned:| 1. 0/1. 0| | Correct Answer(s):| C| 3. If the result of a hypothesis test for a proportion is statistically significant, then A) the null hypothesis is rejected. B) the alternative hypothesis is rejected. C) the population proportion must equal the null value. Feedback: When a hypothesis test is statistically significant then we reject Ho the null hypothesis Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 4. Which of the following conclusions is not equivalent to rejecting the null hypothesis? A) The results are statistically significant. B) The results are not statistically significant.

C) The alternative hypothesis is accepted. D) The p-value < ? (the significance level) Feedback: All are equivalent conclusions for rejecting Ho except when results are not statistically significant (i. e. we do not reject Ho) Points Earned:| 1. 0/1. 0| | Correct Answer(s):| B| 5. Determine if the statement is a typical null hypothesis (Ho) or alternative hypothesis (Ha). There is no difference between the proportion of overweight men and overweight women in America. A) Null hypothesis B) Alternative hypothesis Feedback: Ho refers to no difference or change or equal to.

Ha will be the research hypothesis that involves either a difference, greater than, or less than. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 6. A safety officer wants to prove that ? = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24. 0 mph, with a sample standard deviation of 2. 2 mph. Assume that the speeds of cars are normally distributed. What are the appropriate null and alternative hypotheses? A) Ho: ? = 25 and Ha: ? < 25 B) Ho: ? = 25 and Ha: ? > 25 C) Ho: ? = 25 and Ha: ? ? 25 D) Ho: ? ? 25 and Ha: ? = 25

E) Ho: x-bar = 24 and Ha: x-bar < 24 F) Ho: x-bar = 24 and Ha: x-bar > 24 G) Ho: x-bar = 24 and Ha: x-bar ? 24 H) Ho: x-bar ? 24 and Ha: x-bar = 24 Feedback: The word less is the key term in determining the correct Ha expression. Exceeds implies that the investigator is only interested in whether the true population mean is less than 25. The value of 24 is the sample mean. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 7. An ESP experiment is done in which a participant guesses which of 4 cards the researcher has randomly picked, where each card is equally likely. This is repeated for 200 trials.

The null hypothesis is that the subject is guessing, while the alternative is that the subject has ESP and can guess at higher than the chance rate. The subject actually gets 70 correct answers out of the 200 trials. Which of the following describes the probability represented by the p-value for this test? A) The probability that the subject has ESP B) The probability that the subject is just guessing. C) The probability of 70 or more correct guesses if the subject has ESP. D) The probability of 70 or more correct guesses if the subject is guessing at the chance rate. Feedback: The null hypothesis would be that the subject is guessing, i. . Ho: ? = 1/4. Then the p-value is the probability that if the subject were guessing that they would get 70 or more right Points Earned:| 1. 0/1. 0| | Correct Answer(s):| D| 8. Suppose the significance level for a hypothesis test is ? = 0. 05. If the p-value is 0. 049, the decision is to A) reject the null hypothesis. B) accept the null hypothesis. C) not reject the null hypothesis. Feedback: With p-value <e; ? our decision is to reject the null hypothesis Ho Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 9. Which statement is true about x-bar and ? -hat? A) They are both parameters. B) They are both statistics.

C) x-bar is a parameter and ? -hat is a statistic. D) ? -hat is a parameter and x-bar is a statistic. Feedback: Both x-bar and ? -hat represent statistics. Points Earned:| 0. 0/1. 0| | Correct Answer(s):| B| 10. Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population? A) Values of a parameter will vary from sample to sample but values of a statistic will not. B) Values of both a parameter and a statistic may vary from sample to sample. C) Values of a parameter will vary according to the sampling distribution for that parameter.

D) Values of a statistic will vary according to the sampling distribution for that statistic. Feedback: The population parameter does not vary, however, the values of the statistic will vary based on the sampling distribution of that statistic Points Earned:| 1. 0/1. 0| | Correct Answer(s):| D| 11. For a random sample of 10 men, the mean head circumference is x = 57. 3 cm and the sample standard deviation is s = 2 cm. The standard error of the sample mean is A) 0. 200 B) 0. 447 C) 0. 500 D) 0. 632 Feedback: The standard error equals S/Sq. Rt. of N = 2/3. 16 = 0. 632 Points Earned:| 1. 0/1. 0| |

Correct Answer(s):| D| 12. Suppose that a 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is 35% plus or minus 5%. The margin of error for the confidence interval is A) 5% B) 35% C) 95% Feedback: “plus or minus” indicates the margin of error which is 5% Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 13. In a past General Social Survey, a random sample of men and women answered the question “Are you a member of any sports groups? ” Based on the sample data, 95% confidence intervals for the population proportion who would answer yes are 0. 3 to 0. 19 for women and 0. 25 to 0. 33 for men. Based on these results, you can reasonably conclude that A) at least 25% of American men and American women belong to sports clubs. B) there is no conclusive evidence of a gender difference in the proportions of men and women who belong to sports clubs. C) there is conclusive evidence of a gender difference in proportions of American men and American women who belong to sports clubs. Feedback: Since the two confidence intervals do not overlap there is conclusive evidence that a difference in the proportions exists Points Earned:| 1. 0/1. 0| |

Correct Answer(s):| C| 14. In a past General Social Survey, 87% of a random sample of n = 990 respondents answered yes to the question “Would you approve of an adult male punching a stranger if the stranger had broken into the man’s house? ” A 90% confidence interval for the proportion of all Americans who approve of punching an intruder is A) 0. 852 to 0. 888 B) 0. 849 to 0. 891 C) 0. 845 to 0. 895 D) 0. 842 to 0. 898 Feedback: A confidence interval is found by sample statistic ± Zmultiplier*StandardError. With p-hat of 0. 87, Zmultiplier of 1. 65 and n = 990, the 90% confidence interval is 0. 49 to 0. 891 Points Earned:| 0. 0/1. 0| | Correct Answer(s):| A| 15. A randomly selected sample of n =51 men in Brazil had an average lifespan of 59 years. The standard deviation was 10 years and the standard error was 1. 400. Calculate a 98% confidence interval for the average lifespan for all men in Brazil. A) (55. 6, 62. 4) B) (56. 2, 61. 8) C) (35. 0, 83. 0) Feedback: Using degrees of freedom equal to 51 – 1 gives a t* of 2. 40 for confidence level of 98%. The standard error is equal to s/vn = 10/v51 = 1. 400 [given! ]. The interval then is 59 ± 2. 40*1. 400 = (55. 6, 62. 4) Points Earned:| 1. /1. 0| | Correct Answer(s):| A| 16. In a random sample of 1000 students, 80% were in favor of longer hours at the school library. The standard error of ? -hat is approximately: A) 0. 013 B) 0. 160 C) 0. 640. D) 0. 800 Feedback: The standard error is found by taking the square root of [(0. 80)(0. 20)/1000] = 0. 013 Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 17. A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let ? 1 = average age of onset for women and ? 2 = average age of onset for men.

A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11. 5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4. 5 years. Assume that ages at onset of this disease are normally distributed for each gender, do not assume the population variances are equal. What are the appropriate null and alternative hypotheses? A) ? 1 = ? 2 and Ha: ? 1 ? ?2 B) ? 1 ? ?2 and Ha: ? 1 = ? 2 C) ? 1 = ? 2 and Ha: ? 1 < ? 2 D) ? 1 = ? 2 and Ha: ? 1 > ? 2

Feedback: Since the researcher is interested in detecting only a difference this would imply that any difference will do, thus the Ha is ? Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 18. It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left – right) was found. The alternative hypothesis is one-sided (left hand stronger).

The resulting t-statistic was 1. 90. This is an example of A) a two-sample t-test. B) a paired t-test. C) a pooled t-test. D) an unpooled t-test. Feedback: Since two measurements were taken per individual (i. e. for each man sampled muscle strength was measured on his right hand then his left hand) this would be a study using paired data. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| B| 19. It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true.

To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left – right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1. 90. Assuming the conditions are met, based on the t-statistic of 1. 90 the appropriate decision for this test using ? = 0. 05 and using T-Table is: A) df = 14, so p-value < 0. 05 and the null hypothesis can be rejected. B) df = 14, so p-value > 0. 05 and the null hypothesis cannot be rejected. C) df = 28, so p-value < 0. 05 and the null hypothesis can be rejected.

D) df = 28, so p-value > 0. 05 and the null hypothesis cannot be rejected. Feedback: From T-Table and degrees of freedom equal to 15 ? 1 = 14 and a t-statistic of 1. 90, the p-value is between 0. 025 and 0. 050 which is less than 0. 05 making the appropriate decision to reject Ho. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 20. A shoe company wants to compare two materials, A and B, for use on the soles of boys’ shoes. In this example, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made from Material A and the sole on the other shoe made from Material B.

The sole types were randomly assigned to account for systematic differences in wear between the left and right foot. After three months, the shoes are measured for wear. Let Ho: ? d = 0 versus Ha: ? d ? 0. From this random sample of 10 boys, the sample mean difference was 0. 41 and Sd was 0. 387. If the p-value for this test is 0. 009, then for a significance level of alpha = 0. 05, are the results statistically significant? A) No, results are not statistically significant because the p-value < 0. 05. B) Yes, results are statistically significant because the p-value < 0. 05.

C) No, results are not statistically significant because the p-value > 0. 05 D) Yes, results are statistically significant because the p-value > 0. 05. Feedback: Yes, results are statistically significant because the p-value < 0. 05. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| B| 21. The maximum distance at which a highway sign can be read is determined for a sample of young people and a sample of older people. The mean distance is computed for each age group. What is the most appropriate null hypothesis about the means of the two groups? A) The population means are different.

B) The sample means are different. C) The population means are the same. D) The sample means are the same. Feedback: The null hypothesis, Ho, would indicate that there is no difference and that this would take place in the population. The sample is used to test for a population difference. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| C| 22. The p-value for a one-sided test for a mean was 0. 04. The p-value for the corresponding two-sided test would be: A) 0. 02 B) 0. 04 C) 0. 06 D) 0. 08 Feedback: When we go from a 1-sided test of hypotheses to a 2-sided test we would double the p-value.

Conversely, going from a 2-sided to a 1-sided we would cut the p-value in half. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| D| 23. A shopper wanted to test whether there was a difference in the average waiting times at the check-out counter among 5 different supermarkets. She selected a random sample of 20 shoppers from each of the five supermarkets. What is the alternative hypothesis for this situation? A) The average waiting time to check out is 25 minutes for all five supermarkets. B) The average waiting time to check out is the same for all five supermarkets.

C) The average waiting time for each of the 100 shoppers is different. D) The average waiting time to check out is not the same for all five supermarkets. Feedback: The alternative hypothesis for an ANOVA test is that all the means are not the same, i. e. the means are not all equal. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| D| 24. Which one of the following choices describes a problem for which an analysis of variance would be appropriate? A) Comparing the proportion of successes for three different treatments of anxiety. Each treatment is tried on 100 patients.

B) Analyzing the relationship between high school GPA and college GPA. C) Comparing the mean birth weights of newborn babies for three different racial groups. D) Analyzing the relationship between gender and opinion about capital punishment (favor or oppose). Feedback: The dependent (response) variable needs to be continuous and the different levels of the independent variable need to be mutually exclusive and categorical. This leads to the correct answer of mean birth weights (continuous response) across three racial groups (mutually exclusive, categorical). Points Earned:| 0. /1. 0| | Correct Answer(s):| C| 25. A study compared grade point averages (GPA) for students in a class: students were divided by 6 locations where they usually sat during lecture (i. e. left or right front, left or right center, left or right rear). A total sample size of 12 students was studied (2 students from each section) using one-way analysis of variance. What are the numerator and denominator degrees of freedom for the ANOVA F-test? A) 6 for numerator and 12 for denominator. B) 5 for numerator and 11 for denominator. C) 5 for numerator and 6 for denominator.

Feedback: The numerator degrees of freedom are found by taking the number of group levels minus 1 (this case 6 ? 1 = 5) and the denominator degrees of freedom are found by taking the total sample size minus the number of group levels (12 ? 6 = 6) Points Earned:| 0. 0/1. 0| | Correct Answer(s):| C| 26. A study compared testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. The total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo). A one-way analysis of variance was used to compare the population mean levels for the four sports.

The sum of squared errors is SS Error = 100. What is the value of the Mean Square Error (MS Error)? A) 10 B) 3. 45 C) 3. 85 Feedback: The MS Error is equal to the SS Error divided by the Error degrees of freedom (which are equal to the total sample size minus the number of group levels: 30 ? 4 = 26). Therefore, the answer is 100/26 = 3. 85 Points Earned:| 1. 0/1. 0| | Correct Answer(s):| C| 27. On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA).

There were 235 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. The test F-statistic value is 4. 98. The p-value of 0. 008 is found by calculating: A) the area to the right of 4. 98 under an F-distribution with 2 and 232 degrees of freedom. B) the area to the right of 4. 98 under an F-distribution with 2 and 234 degrees of freedom. C) the area to the right of 4. 98 under an F-distribution with 2 and 231 degrees of freedom.

Feedback: The p-value is the probability of being greater than the F-statistic or simply the area to the right of the F-statistic with the corresponding degrees of freedom for the group (number of group levels minus 1, or 3 ? 1 = 2) and error (total sample size minus the number of group levels, or 235 ? 3 = 232) Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 28. Ninety people with high cholesterol are randomly divided into three groups of thirty, and a different treatment program for decreasing cholesterol is assigned to each group.

The response variable is the change in cholesterol level after two months of treatment. An analysis of variance will be used to compare the three treatments. What null hypothesis is tested by this ANOVA F-test? A) The sample variances are equal for the three treatment groups. B) The population variances are equal for the three treatments. C) The sample means are equal for the three treatment groups. D) The population means are equal for the three treatments Feedback: The null hypothesis for an ANOVA test is that all population means are equal. Points Earned:| 0. 0/1. 0| | Correct Answer(s):| D| 29.

A study done by the Center for Academic Integrity at Rutgers University surveyed 2116 students at 21 colleges and universities. Some of the schools had an “honor code” and others did not. Of the students at schools with an honor code, 7% reported having plagiarized a paper via the Internet, while at schools with no honor code, 13% did so. (Sacramento Bee, Feb 29, 2000, D1. ) For this study, which of the following statements about percent increase in risk is correct? A) There is a 185. 7% increase in the risk of plagiarism at a school with no honor code, compared to a school with an honor code. B) There is an 85. % increase in the risk of plagiarism at a school with no honor code, compared to a school with an honor code. C) There is a 53. 8% increase in the risk of plagiarism at a school with no honor code, compared to a school with an honor code. D) There is a 6% increase in the risk of plagiarism at a school with no honor code, compared to a school with an honor code. Feedback: The percentage increase is found by taking the difference in risks between one group minus the baseline and then dividing this difference by the baseline risk. Here the answer that makes sense is one using the “with honor” as the baseline.

Doing so produces: (13%-7%)/7% = 85. 7% increase in plagiarism from “with honor” to “without honor”. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| B| 30. Which of the following variables COULD be used in a Chi-Square analysis? A) Gender B) Political Party Affiliation C) Race D) Age E) Course Section Number F) All of the above Feedback: All are possible as you could categorize age. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| F| 31. A survey looked at the opinions of 321 respondents from the General Social Survey by whether they owned a gun (or not) and whether they favored (or opposed) a law requiring a permit to own a gun.

What is the correct null hypothesis for this survey? A) There is no relationship in the population between gun ownership and opinion regarding gun law permit B) There is no relationship in the sample between gun ownership and opinion regarding gun law permit C) There is a relationship in the population between gun ownership and opinion regarding gun law permit D) There is a relationship in the sample between gun ownership and opinion regarding gun law permit Feedback: There is no relationship in the population between gun ownership and opinion regarding gun law permit Points Earned:| 1. /1. 0| | Correct Answer(s):| A| 32. Based on the National Household Survey on Drug Abuse, the percentage of 17-year olds who ever tried cigarette smoking is 56. 2%. The relative risk of ever smoking for a 17-year old versus a 12-year old is 3. 6. What is the risk of smoking for a 12-year-old (i. e. what was the percentage of 12-year olds who ever tried smoking)? A) 14. 1% B) 15. 6% C) 50. 0% D) 56. 2% Feedback: You need to use algebra to solve: Relative risk (3. 6) = one group of interest (17 year olds who tried smoking = 56. %) divided by another group of interest (12 year olds who tried smoking and is unknown). Solving for the unknown comes to (3. 6)*(0. 562) = 0. 156 or 15. 6% Points Earned:| 1. 0/1. 0| | Correct Answer(s):| B| 33. A survey examined the opinions of 321 respondents from the General Social Survey by whether they owned a gun (or not) and whether they favored (or opposed) a law requiring a permit to own a gun. What is the correct alternative hypothesis for this survey?

A) There is no relationship in the population between gun ownership and opinion regarding gun law permit B) There is no relationship in the sample between gun ownership and opinion regarding gun law permit C) There is a relationship in the population between gun ownership and opinion regarding gun law permit D) There is a relationship in the sample between gun ownership and opinion regarding gun law permit Feedback: There is a relationship in the population between gun ownership and opinion regarding gun law permit Points Earned:| 1. 0/1. 0| |

Correct Answer(s):| C| 34. A survey examined the opinions of 1447 respondents in the General Social Survey to the question “Do you favor or oppose the death penalty for persons convicted of murder? ” The purpose of examining the data is to see if there is a gender difference in how people would respond to this question. State the null hypotheses for this study. A) There is no relationship in the population between gender and opinion on the death penalty. B) There is no relationship in the sample between gender and opinion on the death penalty.

C) There is a relationship in the population between gender and opinion on the death penalty. D) There is a relationship in the sample between gender and opinion on the death penalty. Feedback: The null hypothesis speaks of no relationship between the variables in the population. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 35. A regression was done for 20 cities with latitude as the explanatory variable (x) and average January temperature as the response variable (y). The latitude is measured in degrees and average January temperature in degrees Fahrenheit.

The latitudes ranged from 26 (Miami) to 47 (Duluth) The regression equation is * y = 49. 4 – 0. 313x The city of Miami, Florida has latitude 26 degrees with average January temperature of 67 degrees Fahrenheit. 1. What is the estimated average January temperature for Miami, and 2. based on the regression equation, what is the residual? A) Estimated January temperature is 36. 88 and the residual is – 11. 88 B) Estimated January temperature is 36. 88 and the residual is 11. 88 C) Estimated January temperature is 41. 3 and the residual is – 25. D) Estimated January temperature is 41. 3 and the residual is 25. 7 Feedback: The estimated January temperature is 41. 3 degrees Fahrenheit. The residual is 25. 7 degrees (residual = observed minus predicted) Points Earned:| 0. 0/1. 0| | Correct Answer(s):| D| 36. Which of the following correlations indicates a stronger linear relationship between two variables? A) – 0. 90 B) 0. 75 C) 0. 50 D) 1. 25 Feedback: The correct answer is -0. 90. Recall that the value of the correlation indicates the strength and this value cannot be less than – 1 nor greater than + 1 (thus ruling out 1. 5 as an answer). The negative sign just indicates the direction of the relationship (positive or negative) and has no bearing on the strength of the relationship. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| A| 37. What is the effect of an outlier on the value of a correlation coefficient? A) An outlier will always decrease a correlation coefficient. B) An outlier will always increase a correlation coefficient. C) An outlier might either decrease or increase a correlation coefficient, depending on where it is in relation to the other points.

D) An outlier will have no effect on a correlation coefficient. Feedback: See the lecture notes! Points Earned:| 1. 0/1. 0| | Correct Answer(s):| C| 38. A group of adults aged 20 to 80 were tested to see how far away they could first hear an ambulance coming towards them. An equation describing the relationship between distance (in feet) and age was found to be: * Distance = 600 – 3 ? Age Based on the equation, what is the direction of the association between distance and age? A) Positive B) Negative C) Zero

D) Direction can’t be determined from the equation. Feedback: The direction of an association can be ascertained by considering the sign of the slope. Since the slope is negative then so is the association. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| B| 39. Past data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from a certain professor is * final exam = 50 + 0. 5 ? midterm For a student with a midterm score of 50, the predicted final exam score is: A) 50.

B) 50. 5. C) 75. D) 100. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| C| 40. Which of the following is a possible values of R2 indicates the strongest linear relationship between two quantitative variables? A) -90% B) 0% C) 80% D) 120% Feedback: Remember that the range of R2 is from 0 to 100%. Thus 80% would indicate the strongest linear relationship, i. e. correlation, based on the square root of 0. 8 is greater than the square root or 0. Points Earned:| 1. 0/1. 0| | Correct Answer(s):| C| Bottom of Form