A recent study of debt among college graduates reported that the average debt ac
ID: 3041432 • Letter: A
Question
A recent study of debt among college graduates reported that the average debt accumulated by graduates of private colleges was $37,200, with a sample standard deviation of $2,046, while the average debt accumulated by graduates of public colleges was S$11,600, with a sample standard deviation of $2,069. The sample sizes were 80 and 240, 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. 0 A. The sample standard devations are not close enough to assume that the population standard deviations could be equal. B. The sample standard deviations are close enough to assume that the population standard deviations are equal. ° C. The sample standard deviations are not exactly equal, so the population standard deviations cannot be equal. D. The sample standard deviations and sample sizes are not exactly equal, so the population standard deviations cannot be equal. b. Conduct a hypothesis test to determine if the average college debt for bachelor of arts degree recipients is at least $21,000 more for graduates from private colleges than from public colleges. Use a significance level of = 0.025. Let x1 =$37.200 and x2 = $11,600. State the null and altemative hypotheses. OA. Ho : 1-2#821,000 C. Ho:m-u2 >$21,000 E. H0: 1-u2 $21,000 Calculate the test statistic.Explanation / Answer
The statistical software output for this problem is:
Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 21000
HA : 1 - 2 < 21000
(with pooled variances)
Hypothesis test results:
Hence,
a) Option B is correct.
b) Hypotheses: Option D is correct.
Test statistic = 17.27
P - value = 1
Concusion: Option D is correct.
Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 25600 266.37219 318 17.26907 1