Question

A recent study of debt among college graduates reported that the average debt accumulated by graduates of private colleges was ​$38,100 with a sample standard deviation of $2,042 while the average debt accumulated by graduates of public colleges was ​$11,800 with a sample standard deviation of $2,110 The sample sizes were 60and 190​, respectively. Complete parts a and b below.

a. Examine the sample standard deviations. What do these suggest is the relationship between the two population standard​ deviations? Support your assertion.

(Multiple Choice)

A.

The sample standard deviations are close enough to assume that the population standard deviations are equal.

B.

The sample standard deviations and sample sizes are not exactly​ equal, so the population standard deviations cannot be equal.

C.

The sample standard deviations are not exactly​ equal, so the population standard deviations cannot be equal.

D.

The sample standard devations are not close enough to assume that the population standard deviations could be equal.

b. Conduct a hypothesis test to determine if the average college debt for bachelor of arts degree recipients is at least ​$24,000 more for graduates from private colleges than from public colleges.

Use a significance level of alpha equals 0.05.

1. State Null hypothesis

2. Calculate test statistic

3. Calculate p-value

4. State conclusion for this hypothesis test

Answer 1