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# Stat 250 Review

Final Exam Review Part VI Definitions and Terms: Know the major definitions and terms for example 1.2.3.

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4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Population Sample Descriptive Statistic Inferential Statistics Parameter vs Statistics Variable a. Categorical Statistic estimates Parameter b. Quantitative estimates , sample mean , population i. Discrete mean s, sample standard estimates , population ii. Continuous deviation standard deviation Random Variable estimates P, population ? p , sample Sampling Distributions proportion proportion

Parameter (Defines a population) Statistic (calculated from sample to estimate a parameter) Central Limit Theorem Law of Large Numbers Confidence Level (1- )*100 Type I error (rejecting the null hypothesis when in fact it is true) Type II error (not rejecting the null hypothesis when in fact the null is not true) What is true What you did Do not Reject H0 Reject H0 H0 true No Error Type I error Ha True Type II Error No Error 15. Level of Significance (The probability of making a Type I error) 16. Interpretation of a confidence interval 17. P-value a.

The probability of making a type I error based on your sample b. The probability, computed supposing the H0 to be true, that the test statistic will take a value at least as extreme as that actually observed. 18. Interpretation of a test of significance (hypothesis test) Types of Problems 1. Reading and interpreting graphs (make sure you read the labels so you know units and whether the graph is frequency (counts) or relative frequency (percents, ratios, probabilities). 2. Calculating Measures of Center a. Mean b. Median 3. Calculating Measures of Spread a. Range b.

You will not have to calculate the standard deviation, but you must understand what the standard deviation is – the average distance each data value is from the mean. c. Interquartile Range (Q3 – Q1) i. 1st quartile ii. 2nd quartile (median) iii. 3rd quartile 4. Shape of distributions 5. Shape of distributions and effects on Mean and Median 6. Effects of outlier and skewed distribution a. Non-resistant measures of Center and Spread: mean and standard deviation b. Resistant measures of Center and Spread: median and interquartile range 7. Boxplot and 5 number summary: Min, Q1, Q2, Q3, Max 8.

Binomial Distribution a. Calculating the mean , =np np(1 p) b. Calculating the standard deviation, c. Finding probabilities using the CDF output from MINITAB 9. Calculating Probabilities for a Normal distribution (Knowing how to use Table A, the standard normal distribution) a. Standardizing any normal random variable i. z x b. Unstandardizing any normal random variable i. x z 10. Sampling distributions a. Sampling distribution of the sample mean – samples of size n i. Mean, x= (can be calculated even if we do not know the shape of the distribution) ii. Standard deviation, x n the shape of the distribution) can be calculated even if we do not know iii. Shape of sampling distribution 1. If population the sample came from is normal, all sampling distributions of any size are normal 2. If the shape of the population is unknown or is NOT normal, then the sampling distribution of the sample mean is normal only if the sample size is 30 or more by the Central Limit Theorem (The shape of the sampling distribution becomes approximately Normal if the sample size is large enough. In our class a sample of size 30 or more is “large enough” to assume the sampling distribution is approximately Normally distributed. iv.

Knowing how to compute probabilities based on the sampling distribution of the sample mean when applicable. v. Inferential Techniques based on sampling distribution when conditions are met (SRS and Normality) 1. Estimation – Confidence Intervals : statistic margin of error (margin of error = critical value * standard error) a. known: i. X z /2 * n ii. Sample size: We can determine the sample size needed so that a specific margin of error is observed at a specified confidence level: n b. z unknown: X * m 2 /2 t / 2,df * s n 2. Significance Tests (Hypothesis Tests) a. nown: test statistic, z0 X 0 n b. unknown: test statistic, t0 X s 0 n b. Sampling distribution of the sample proportions – samples of size n i. Mean, p (can be calculated even if we do not know the shape of the ? p distribution) ii. Standard deviation, p(1 P) (can be calculated even if we do not n ? p know the shape of the distribution iii. Shape of sampling distribution of the sample proportions becomes approximately normal if (our book states: np? 10 and n(1-p)? 10, that is the sample successes and failures must be 10 or more. ) np(1-p)? 10 , which is conservative. iv.

Inferential Techniques based on sampling distribution when conditions are met (SRS and Normality) 1. Estimation – Confidence Intervals : statistic margin of error (margin of error = critical value * standard error) a. ? pz /2 * ? ? p (1 p ) n i. Sample size: We can determine the sample size needed so that a specific margin of error is observed at a specified confidence level: n p(1 p) z /2 m 2 If a prior estimate for p is known, use it. If a prior estimate is not know, use p = 0. 5 2. Significance Tests (Hypothesis Tests) a. known: test statistic, z0 ? p p0 p0 (1 p0 ) n 11.

Inferential techniques for 2 sample problems (means and proportions – on PowerPoint that is coming next) which are also based on Sampling distribution when conditions are met. a. You will be given the value of the standard error for two sample problems (two sample means dependent, you will be given the standard deviation of the differences, but you will have to calculate the standard error s .) n b. You will have to calculate the pooled proportion for the two sample proportions ? problems: p x1 x2 n1 n2 c. You will have to calculate confidence intervals and do tests of significance (hypothesis tests) 2. Goodness of fit test Best Way to Study 1. 2. 3. 4. 5. Go over Test 1 and Test 2 Go over all quizzes since Test 2 Go over all your quizzes Go over Post-Tests Go over Homework What you need for the final 1. 2. 3. 4. Pencil and eraser Calculator Table A and Table C Formula Sheet: you have two choices. You must choose either A or B a. HAND WRITTEN formula sheet – no copies. Must be the original. On an 8X11 sheet of paper, front and back, you can write whatever you wish. Hand written!!! b. Pristine, no writing on it, copy of the formula sheet on Blackboard. Scantron will be provided.

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