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.
-In order to construct a confidence interval estimate for the difference between two population means,independent samples are obtained from two normal populations with unknown but assumed to be equal variances.If the first sample contains 18 items and the second sample contains 14 items,which of the following distributions will be used?
A)the t distribution with 32 degrees of freedom
B)the t distribution with 17 degrees of freedom
C)the t distribution with 13 degrees of freedom
D)the t distribution with 30 degrees of freedom

Question

Quizplus · Accepted Answer

The degrees of freedom for the t distribution when assuming equal variances is calculated as (n1 + n2 - 2). Here, n1 = 18 and n2 = 14, so the degrees of freedom is 18 + 14 - 2 = 30.