Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately of = 5.1. Suppose a recent study of age at first marriage for a random sample of 41 women in rural Quebec gave a sample variance s= = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1. (a) What is the level of significance? 0.05 State the null and alternate hypotheses. O Ho: 02 = 5.1; H,: 02 = 5.1 O Ho: 02 = 5.1; H,: 02 > 5.1 O Ho: 02 = 5.1; H,: 02 0.100 O 0.050 0.100 O 0.050 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value S a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, the evidence is sufficient to conclude that the subject distribution of books in the library is different from that of books checked out by students. O At the 5% level of significance, the evidence is insufficient to conclude that the subject distribution of books in the library is different from that of books checked out by students.The type of household for the U.5. population and for a random sample of 411 households from a community in Montana are shown below. Married with children 26% 1130 Married, no children 29% 111 Single parent 9% 37 One person 25% 94 Other (e.g., roommates, siblings} 11% 59 Use a 5% level of signicance to test the claim that the distribution of U.S. households ts the Dove Creek distribution. (a) What is the level of signicance? I105 J State the null and alternate hypothews. O Ho: The distributions are different. H1: The distributions are the same. 0 Ho: The distributions are the same. H1: The distributions are the same. 0 Ho: The distributions are different. H1: The distributions are different. 9 H0: The distributions are the same. H]: The distributions are different. I F' theyalue ofti'le chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.) cted frequencies greater than 5? Yes O No I What sampling distribution will you use? Q chisquare 0 Student's t 0 normal 0 binomial O uniform