Homework for the week 11 applied class DUE Monday, week 12 Name: ID 1. If X ~ Bin(n, p) what is the approximate distribution of X for large sample size? X ~ AND what specific conditions are necessary for this approximation to be valid? 2. If a sample of size n is taken from a population with probability of success p, what is the approximate distribution of the sample proportion p? p~ 3. During one of the AFL football season, the "Home Team" won 49 of the 82 games played outside of Melbourne. Is this strong evidence of a home field advantage in professional AFL football? That is, does the home team (outside Melbourne) win more than 50% of its games? Use an appropriate hypothesis test to make your decision to a level of significance of 5%. Show all steps: [See Lecture 27, page 1] a) Sample proportion = (keep 3 sig. figures at least) b) Hypotheses: c) Check conditions: d) Standardized test-statistic, z-statistic = e) p-value = f) Decision and Conclusion