A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you wanted to test whether the average balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?
A) There is not evidence that the average balance is $75.
B) There is evidence that the average balance is $75.
C) There is evidence that the average balance is not $75.
D) There is not evidence that the average balance is not $75.

Question

Quizplus · Accepted Answer

To test whether the average balance is different from $75, we need to conduct a two-tailed hypothesis test. The null hypothesis is that the average balance is $75, and the alternative hypothesis is that the average balance is different from $75.

Since the sample size is large (n=100) and the population standard deviation is unknown, we can use a t-test with the t-distribution. The test statistic is calculated as:

t = (x̄ - μ) / (s / √n) = (83.40 - 75) / (23.65 / √100) = 3.51

Using a two-tailed test at a 5% significance level with df = 99 (n-1), the critical values are ±1.984. Since the calculated t-value (3.51) is greater than the critical value (1.984), we reject the null hypothesis.

Therefore, we can conclude that there is evidence that the average balance is not $75.

A Manager of the Credit Department for an Oil Company