1. A large insurance company wants to determine whether theproportion of male policyholders who would not submit autoinsurance claims of under $500 is the same as the proportion offemale policyholders who do not submit claims of under $500. Arandom sample of 400 male policyholders produced 272 who had notsubmitted claims of under $500, whereas a random sample of 300female policyholders produced 183 who had not submitted claims ofunder $500
a) Construct a 90% confidence interval for the differencebetween the proportions of males and of females who had notsubmitted auto insurance claims of under $500.
b) Find the p-value of the appropriate test.
In a random sample of 10 LAS students, the sample mean timespent studying during a particular week was 15.7 hours with samplestandard deviation 3.1 hours. In a random sample of 8 Engineeringstudents, the sample mean time studying during the same week was20.2 hours per month with sample standard deviation 4.4 hours.Assume that the two populations are normally distributed.
a) Assume that the two population variances are equal. Constructa 95% confidence interval for the difference between the overallaverage times Engineering and LAS students spent studying duringthis week.
b) Since the larger sample variance is more than twice as big asthe smaller one, the assumption of equal variances is questionablehere. Construct a 95% confidence interval for the differencebetween the overall average times Engineering and LAS studentsspent studying during this week without assuming that the twopopulation variances are equal. Use Welch’s T.
