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Review of Hypothesis Testing Types of Tests 1) 1-Sample z 2) 1-Sample t 3) 2-Sample t 4) 1-Proportion 5) 2-Proportion 6) Paired t-test 7) Chi-Square G.O.F test 8) Chi-Square Test of Independence 9) Linear Regression t-test Universal Conditions 1. Randomization Condition: The sample should be a simple random sample of the population. 2. 10% Condition: (Independence) If sampling has not been made with replacement, and you are drawing from a finite population then the sample size, n, must be no larger than 10% of the population. 1-Sample-Z Test • Quantitative Data • You know (sigma) the standard deviation of the population. • Normality Check: Stated in the question, probability plot, n is at least 30. 1-Sample t-test • Quantitative Data • You do not know (sigma) the standard deviation of the population. • You use “s” the standard deviation of the sample to approximate sigma. • Normality Check: (Central Limit Theorem) Sample Size of at least 30 2-Sample t-test • 2 Sets of Quantitative Data • You do not know (sigma) the standard deviation of either population. • You use s1 and s2 to approximate sigma for both populations. • Normality Check: (CLT) Both sample sizes are at least 30. 1-Proportion • (Categorical Data) Qualitative Data • You use p-hat and q-hat to approximate the standard deviation of the population. pq n • Normality Check: The sample size has to be big enough so that both np and nq are at least 10. 2-Proportion • 2 Sets of (Categorical Data) Qualitative Data • You use p-hat and q-hat to approximate the standard deviation for both populations. p1q1 n1 p2 q2 n2 • Success/Failure Condition: The sample size has to be big enough so that both n1p1, n1q1 n2p2, n2p2 are at least 10. Paired t-test • Quantitative Data • Same as a one sample t-test but you have two pieces of data for each subject or experimental unit. • Usually (Pre-Test/Post-Test) • Normality Check: (CLT) “n” is at least 30 Chi-Square Goodness of Fit • When you are comparing multiple proportions for a distribution. (M & M project) • Conditions: • No expected counts less than 5. • All variables are independent. Expected Counts equal sample size multiplied by the %’s stated in the model. Chi-Square Test of Independence • When you are comparing two categorical variables. (Two Way Table) • Conditions: • No expected counts less than 5. • All values are independent. Finding Expected Counts The expected count in any cell of a two-way table when H0 is true is row total column total expected count = table total Linear Regression t-test Conditions for Regression Inference Suppose we have n observations on an explanatory variable x and a response variable y. Our goal is to study or predict the behavior of y for given values of x. • Linear The (true) relationship between x and y is linear. For any fixed value of x, the mean response µy falls on the population (true) regression line µy= α + βx. The slope b and intercept a are usually unknown parameters. • Independent Individual observations are independent of each other. • Normal For any fixed value of x, the response y varies according to a Normal distribution. • Equal variance The standard deviation of y (call it σ) is the same for all values of x. The common standard deviation σ is usually an unknown parameter. • Random The data come from a well-designed random sample or randomized experiment.