Question

Graduates A random sample of the average debt (in dollars) at graduation from 30 of the top 100 public colleges and universities is listed below. Is there sufficient evidence at a _ 0.01 to conclude that the population mean debt at graduation is less than $18,000? Assume s _ 2605

16,012 15,784 16,597 18,105 12,665 14,734
17,225 16,953 15,309 15,297 14,437 14,835
13,607 13,374 19,410 18,385 22,312 16,656
20,142 17,821 12,701 22,400 15,730 17,673
18,978 13,661 12,580 14,392 16,000 15,176
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results

Answer 1

H0 : μ = 18000

H1 : μ < 18000 - - - > Claim

Test value = - 3.578

Critical value = ±2.58

There is significant evidence to accept the claim that mean debt at graduation is less than $18000

Explanation:

H0 : μ = 18000

H1 : μ < 18000

From the data:

Sample size, n = 30

Sample mean, x = 16298.37

The test statistic :

(16298.37 - 18000) ÷ (2605/sqrt(30))

−1701.63 / 475.60575

= - 3.578

The critical value :

Using the standard normal table;

Critical value at α = 0.01

Critical value = ±2.58

Decison region :

|test statistic | > |Critical value | ; reject H0

|3.578| > |2.58| ; We reject H0 and conclude that Mean debt at graduation is less than $18000