Create a confidence interval for the difference between two means.
-Data were collected on annual personal time (in hours) taken by a random sample of 16
Women and 7 men employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men
Took an average of 21.89 hours of personal time per year with a standard deviation of 3.29
Hours. The correct 90% confidence interval for the difference between women and men in
The average number of hours of personal time taken per year is
A) 0.30 to 5.48 hours.
B) -0.50 to 3.21 hours.
C) -4.67 to -0.62 hours.
D) 1.27 to 6.89 hours.
E) None of the above.

Question

Quizplus · Accepted Answer

The correct answer is A because the 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is 0.30 to 5.48 hours. This interval was calculated using the formula:CI = (x1 - x2) ± z * sqrt((s1^2/n1) + (s2^2/n2))where:x1 = the sample mean of the first group (women)x2 = the sample mean of the second group (men)s1 = the sample standard deviation of the first group (women)s2 = the sample standard deviation of the second group (men)n1 = the sample size of the first group (women)n2 = the sample size of the second group (men)z = the z-score corresponding to the desired confidence level (90% in this case)Plugging in the values from the given data, we get:CI = (24.75 - 21.89) ± 1.645 * sqrt((2.84^2/16) + (3.29^2/7))CI = 2.86 ± 1.645 * sqrt((0.5046) + (1.4361))CI = 2.86 ± 1.645 * 1.318CI = 2.86 ± 2.16CI = (0.30, 5.48)Therefore, the correct answer is A.

Create a Confidence Interval for the Difference Between Two Means