THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A career counselor is interested in examining the salaries earned by graduate business school students at the end of the first year after graduation.In particular,the counselor is interested in seeing whether there is a difference between men and women graduates' salaries.From a random sample of 20 men,the mean salary is found to be $42,780 with a standard deviation of $5,426.From a sample of 12 women,the mean salary is found to be $40,136 with a standard deviation of $4,383.Assume that the random sample observations are from normally distributed populations,and that the population variances are assumed to be equal.
-What is the lower confidence limit of the 95% confidence interval for the difference between the population mean salary for men and women?
A)-$1,135.781
B)-$791.792
C)-$952.833
D)$834.835

Question

Quizplus · Accepted Answer

The correct answer is A because the lower confidence limit of the 95% confidence interval for the difference between the population mean salary for men and women is -$1,135.781. This is calculated using the formula:Lower confidence limit = (x̄1 - x̄2) - t*√((s1^2/n1) + (s2^2/n2))where x̄1 and x̄2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and t is the t-value from the t-distribution with (n1 + n2 - 2) degrees of freedom and a significance level of 0.05.