II. Probability P(AUB) = P(A) + P(B) - P(An B) P(AB) = P(An B) P(B) E(X) = Ux = Expi Var(X) = 0; = _(x - ux)2pi If X has a binomial distribution with parameters n and p, then: P(X = k) = k) p* (1 - p)" -* HI = np Or = Vnp(1 - p) Ho = P Op = P(1- p n If x is the mean of a random sample of size n from an infinite population with mean u and standard deviation O, then: MY = HIII. Inferential Statistics Standardized test statistic: statistic - parameter standard deviation of statistic Confidence interval: statistic + (critical value) . (standard deviation of statistic) Single-Sample Statistic Standard Deviation of Statistic Sample Mean Sample Proportion p(1 - p) n Two-Sample Statistic Standard Deviation of Statistic Difference of sample means 722 Special case when 61 =02 ol+1 n2 Difference of PI (1 - PI) + P2 (1 - P2) sample proportions n1 n2 Special case when P1 = P2 Jp(1 - P) 1 + 1 Vn, n2 Chi-square test statistic = \\ (observed - expected) expected\fD Question 30 1 pts Which of these is not a typical part of a write up for a hypothesis test? State the null hypothesis and alternative hypothesis in the context of the problem. Identify the type of test and check that the conditions are met for it to be used. Sketch the distribution, and identify the P-value and rejection region. State your conclusion in the context of the problem. Construct and interpret a confidence interval.D Question 28 1 pts The data given below represents the results of a survey of 200 men and 300 women. Participants were asked whether they preferred to spend free time watching movies, reading books, or playing sports. Imagine you wish to determine if the data provides sufficient evidence that men and women's preferences are distributed differently. Movies Books Sports Men 65 61 74 Women 88 116 96 With a tolerance of a = 0.10, which of these best describes the results of the hypothesis test? O 0.15