Statistics 301: Hypothesis Testing and P-values, Exams of Statistics

Download Statistics 301: Hypothesis Testing and P-values and more Exams Statistics in PDF only on Docsity! STATISTICS 301 TA: Perla E. Reyes DISCUSSION 2 Pag. 1 Review 1. RECALL Skeptic’s Argument the treatments do not make a difference. Some subjects will yield a success regardless of the treatment they receive, and the others will yield a failure regardless of the treatment they receive. 2. RECALL Step 1: The Hypotheses. The null hypothesis is H0 : p1 = p2. (The skeptic is correct.) There are 3 choices for the alternative hypothesis : (1) 1st Alternative H1 : p1 > p2. (2) 2nd Alternative H1 : p1 < p2. (3) 3rd Alternative H1 : p1 6= p2. 3. Step 2: The Test Statistic and its Sampling Distribution. • The Test Statistic is the number that summarizes the information in the data that is relevant to the problem of deciding between the hypotheses. • The Test Statistic is the sample proportion of successes on the first treatment minus the proportion of successes on the second treatment. x = p̂1 − p̂2 • The Sampling Distribution of the test statistic X provides two types of information, namely, all the possible values of the test statistic x′s and their corresponding probabil- ities P (X = x) (see computation of probabilities) assuming that the null hypothesis H0 is true. • The Sampling Distribution table MIGHT contain 2 additional columns: P (X ≤ x) and P (X ≥ x) Example: x P (X = x) P (X ≤ x) P (X ≥ x) -1 16 = 0.1667 1 6 = 0.1667 6 6 = 1.0000 0 46 = 0.6667 5 6 = 0.8333 5 6 = 0.8333 1 16 = 0.1667 6 6 = 1.0000 1 6 = 0.1667 • Successive values of the test statistic differ by a constant amount called δ ”delta” (low- ercase Greek letter delta) δ = n n1n2 • If n1 = n2 or m1 = m2, the sampling distribution is symmetric around zero. reyes@stat.wisc.edu. www.stat.wisc.edu/∼reyes/ B248MSC: W 3:00pm, F 2:00pm