The proportions of yearly sales across a province in Canada for four popular hiking shoe brands (Merrell, Keen, The North Face, and Saucony, in terms of pairs of shoes sold per year) were found to be 50 percent, 30 percent, 11 percent, and 9 percent, respectively. Suppose that a new survey of 1,000 shoppers in a city in that province was conducted and the following purchase frequencies were found: Merrell: 510 Keen: 300 The North Face: 120 Saucony: 70 Suppose you are interested in testing the null hypothesis that the population proportion of consumers who prefer each brand province-wide match the population proportion of customers who prefer each brand within the city. Which type of test is most appropriate? A chi-square test of homogeneity An ANOVA F-test A t-test for the population slope O A chi-square test (multinomial probabilities) QUESTION 2 Select the most appropriate set of null and alternative hypotheses. Ho: P1 = 0.50, p2 = 0.30, p3 = 0.11, p4 = 0.09; Ha: at least one of p1 , P2, P3 and P4 is not equal to the value stated in Ho Ho: P1 = 0.50, p2 = 0.30, p3 = 0.11, p4 = 0.09; Ha: P1 # 0.50, p2 # 0.30, p3 # 0.11, p4 # 0.09 Ho: H1 = 0.50, H2 = 0.30, M3 = 0.11, H4 = 0.09; Ha: at least one of H1, M2, M3, M4 is not equal to the value stated in Ho Ho: H1 = 0.50, H2 = 0.30, M3 = 0.11, H4 = 0.09; Ha: M1 # 0.50, M2 # 0.30, M3 * 0.11, M4 = 0.09QUESTION 3 Calculate the expected cell frequency (E ) for Merrell shoes. QUESTION 4 Calculate the chi-square test statistic. QUESTION 5 Suppose the critical value for this test is 7.81473. Select the most appropriate conclusion. O Since the test statistic is greater than the critical value, we reject the null hypothesis. Since the test statistic is less than the critical value, we reject the null hypothesis. Since the test statistic is greater than the critical value, we do not reject the null hypothesis. Since the test statistic is less than the critical value, we do not reject the null hypothesis. QUESTION 6 Select the most appropriate interpretation. O The population proportion of city-wide customers is significantly different from the population proportion of province-wide customers for at least one of the four brands of hiking shoes. The population proportion of city-wide customers is significantly different from the population proportion of province-wide customers for all of the four brands of hiking shoes. The population proportion of city-wide customers is not significantly different from the population proportion of province-wide customers for at least one of the four brands of hiking shoes. D The population proportion of city-wide customers is not significantly different from the population proportion of province-wide customers for all of the four brands of hiking shoes