2Data gathered by the U.S Department of Transportation show the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 50 Buffalo residents the mean is 22.5 miles a day and the standard deviation is 8.4 miles a day, and for an independent simple random sample of 100 Boston residents the mean is 18.6 miles a day and the standard deviation is 7.4 miles a day.
i. What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day?
ii. What is the 95% confidence interval for the difference between the two population means?
iii. Are all the requirements to build a confidence interval for the differences of mean satisfied?
PROBLEM 4: The Educational Testing Service has conducted studies designed to identify differences between the scores of male and female students on the SAT. For a sample of female students, the standard deviation of test scores was 83 on the verbal portion of the SAT. For a sample of male students, the standard deviation was 69 on the same test. The standard deviations were based on SRS of 121 male and 121 female students.
i. Does the data indicate a difference between the variances of female and male students’ scores on the verbal portion of the SAT? Use a 1% level of significance. Use the critical value method.
ii. What is the p−value?
iii. Would the decision be the same if you tested at a 5% level of significance? Consider the p−value from (ii). What would be the lowest significance level at which you could reject H0?
PROBLEM 5: A sample of 1545 men and a sample of 1691 women were used to compare the amount of housework done by women and men in dual-earner marriages. The study showed that 67.5% of the men felt the division of housework was fair and 60.8% of the women felt the division of housework was fair.
i. Is the proportion of men who felt the division of housework was fair greater than the proportion of women who felt the division of housework was fair? Test your hypothesis at the 5% level of significance. Use the p−value method.
ii. Use the confidence interval method to test the hypothesis. Show all steps.