Statistics 301 Discussion 2: Skeptic's Argument and Hypothesis Testing, Exams of Statistics

Download Statistics 301 Discussion 2: Skeptic's Argument and Hypothesis Testing and more Exams Statistics in PDF only on Docsity! STATISTICS 301 TA: Perla E. Reyes DISCUSSION 2 Pag. 1 Review 1. 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. Hypothesis Testing • Step 1: The Hypotheses. The null hypothesis is H0 : p1 = p2. (The skeptic is correct.) There are 3 choices for the alternative hypothesis : (1) H1 : The 1st treatment is superior to the 2nd treatment p1 > p2. (2) H1 : The 2nd treatment is superior to the 1st treatment p1 < p2. (3) H1 : The 1st treatment is either superior or inferior to the 2nd treatment p1 6= p2. The default alternative hypothesis is (3). Choose (1) or (2) when the other direction is inconceivable. • 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 Computation of Probability in the equally likely case, P (any particular outcome) = 1 the number of all the possible outcomes – Any specified collection of outcomes is called event P (an event) = the number of outcomes in the event the number of all the possible outcomes – The Sampling Distribution of the test statistic X provides two types of infor- mation, namely, the possible values of the test statistic and their corresponding probabilities assuming that the null hypothesis H0 is true. Example: x P (X = x) -1 16 0 46 1 16 Practice Problem 1. Text Book, p-57, problems 1.(a) and 3. 2. Extra Homework, p-1, problem 2. reyes@stat.wisc.edu. www.stat.wisc.edu/∼reyes/ B248MSC, MW 11:00-12:00