13. (0.5 + 0.5 + 0.5 + 0.5 + 2 = 4 marks) A study was conducted to compare the length of time between men and women to assemble a certain product. Sample standard deviation in a random sample of times for 10 men was 3.3 minutes, and sample standard deviation in a random sample of times for 8 women was 1.6 minutes. Past experience indicates that population of lengths of time is normal for both men and women. Is it sufficient sample evidence to conclude that the variance of the lengths of time for men is larger than the variance of the lengths of time for women? In a - d, test the appropriate hypotheses at =005 level of significance using critical value approach. Use the ratio of the sample variance in the sample of times for men and sample variance in the sample of times for women Sll / 322 as test statistic. a. State null and research hypotheses H,: HI: b. The observed value of test statistic is ./ obs. c. State the rejection region (in the form of inequality) d. Decide whether null hypothesis is rejected or is not rejected at & =005 , and insert the word rejected or the words not rejected into the following statement. Null hypothesis is at a =005 Insert the word sufficient or insufficient into the following statement. There is sample evidence to conclude that the variance of the lengths of time for men is larger than the variance of the lengths of time for women. e. Construct a 90% confidence interval for the ratio of two population variances. Insert the missing numbers, which are endpoints of 90% confidence interval for the ratio of two population variances. Keep two digits after decimal point in the answer. The formula for (1-a)100% confidence interval for the ratio of two population variances is given below. Jal2, n-1, 12-1 Ja/2, n, -1, 1-1 Jal, n,-1, n,-1 S 2 fa12, n - 1, 1-1 Show your work in finding endpoints of confidence interval