Question

According to the report by the​ government-lending institution, college students who have credit cards have an average credit card balance of ​$1,076. A random sample of 40 college students was​ selected, and their average credit card debt was found to be ​$1,436. Assume the standard deviation for student credit card debt is ​$276. Using α=0.10​ to complete parts a and b below.

a. Does this sample provide enough evidence to challenge the findings by Sallie Mae?
b. Determine the p-value for this test.

Answer 1

Kindly check explanation

Explanation:

Given the following :

Population mean (μ) = 1076

Sample mean (m) = 1436

Number of samples (n) = 40

Population standard deviation (sd) = 276

α=0.10

Null: μ = 1076

Alternative : μ > 1076

This is a right tailed test;

Reject null;

If z > z0.10

Z0.10 = 1.28 ( right tailed)

Test statistic (z) :

(m - μ) / (σ / √n)

(1436 - 1076) / (276 / √40)

360 / 43.639431

= 8.249

Since

8.249 > 1.28

We reject the null.

B) using the p value calculator from Zscore and alpha level

Zscore = 8.249 ; α=0.10, one tailed

P value < 0.00001

Which shoes that result is significant at 0.10