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

Question

Quizplus · Accepted Answer

The null hypothesis is that the mean monthly balance of credit card holders is $75. Since we are conducting a two-tailed test (we are simply testing for the mean being different than $75, not specifically greater or less than $75), we will reject the null hypothesis if the sample mean is significantly above or below $75. Since the sample mean is $83.40 and the sample standard deviation is $23.65, we can perform a t-test to determine the p-value. Assuming a significance level of 0.05, our calculated p-value is extremely small which means that we can reject the null hypothesis. Therefore, we can conclude that there is evidence that the mean balance is not $75.

A Manager of the Credit Department for an Oil Company