STAT 509 -- EXAM 2 REVIEW SHEET I. Confidence Intervals and Estimation A. Estimation of a Parameter 1. Point Estimation 2. Unbiased statistic 3. Standard Error of a Statistic B. Precise Interpretation of a Confidence Interval 1. What does, for example, "95 percent confidence" mean exactly? C. Relationship among confidence level, sample size, and width of the CI D. Confidence Intervals about a Mean (when sigma unknown) 1. Sampling distribution of "t-statistic" (t distribution) 2. How is t distribution different from standard normal? 3. Reading Table 2 to get critical t values 4. Using Formula for CI for mu F. Sample Size Determination for CI about mu II. Hypothesis Tests A. Purpose of Hypothesis Testing 1. Null and alternative hypotheses a. Which one is "assumed" to be true before the test? b. Which one are we "trying to prove" (seeking evidence for)? 2. Type I error 3. Significance level (alpha) for a hypothesis test 4. How do we decide whether to reject H_0 (whether result is "significant")? B. One-sample t-test 1. Test statistic t a. What distribution does t have if H_0 is true? (degrees of freedom?) 2. When do we reject H_0? a. One-tailed alternative (>) b. One-tailed alternative (<) c. Two-tailed alternative (not equal) d. Reading Table 2 3. Stating conclusions in terms of the variables in the problem 4. Assumptions and Robustness of the t procedures a. When can we safely use the t procedures? C. P-values 1. Precise definition of P-value 2. What does p-value tell us about the evidence against H_0? D. Practical Significance and Statistical Significance E. Relationship between a CI and a Two-sided Hypothesis Test about mu F. Power of a Hypothesis Test 1. Type I and Type II errors 2. Definition of Power 3. Calculating the power of a test about mu (with sigma known) III. More Inference A. Confidence Intervals about a Proportion 1. Definition of Sample proportion (p-hat) 2. Sampling Distribution of p-hat 3. Large-sample CI for p 4. When can we use this formula? (rules of thumb) B. Hypothesis Test About a Proportion 1. Test Statistic z a. What distribution does z have if H_0 is true? 2. Determining rejection region (for each type of alternative) 3. Stating conclusions in terms of the variables in the problem C. Other Confidence Intervals and Tests 1. Confidence interval for the variance sigma^2 (and for sigma) 2. Test about the variance sigma^2 a. Assumptions of these procedures b. Are these procedures robust? 3. F-Test comparing two variances IV. Inference in Two-Sample Situations A. Paired Samples 1. What kinds of studies yield paired data? (Examples) 2. Key characteristic of paired samples 3. Performing Inference about the Mean of the Differences 4. t-test about delta 5. CI about delta 6. How does the paired-data problem reduce to a one-sample problem? B. Independent Sample Problems 1. Key difference between Independent Samples and Paired Samples 2. Comparing Two Population Means a. Assumptions b. Equal-variance case and unequal-variance case 3. CI for mu_1 - mu_2 4. t-test of H_0: mu_1 = mu_2 a. test statistic t b. Determining correct degrees of freedom c. Finding rejection region and making correct conclusion 5. Comparing Two Proportions a. Sampling distribution of p_1-hat - p_2-hat b. Assumptions for the approximate normality to be valid 6. Hypothesis test of p_1 = p_2 a. test statistic z b. pooled sample proportion p-hat c. Finding rejection region and making correct conclusion V. Analysis of Variance (ANOVA) with a Completely Randomized Design A. Basic Terms 1. Designed Experiment vs. Observational Experiment 2. Response Variable 3. Factors (Quantitative and Qualitative) 4. Levels of a Factor 5. Treatments 6. Experimental Units 7. Three Principles of Experimental Design B. Completely Randomized Design 1. Hypothesis Test for whether all treatment means are equal 2. Comparing variance WITHIN groups to variance BETWEEN groups 3. SST, SSE, MST, MSE (What do these quantities measure?) 4. The ANOVA F-statistic: F = MST/MSE a. What is its distibution if H_0 is true? b. How do we use it to test whether all treatment means are equal? 5. Summarizing the data with an ANOVA table 6. Assumptions of ANOVA F-test 7. Rejection region and proper conclusions for ANOVA F-test 8. Tukey's Multiple Comparisons Procedure