The loan manager for State Bank and Trust has claimed that the mean loan balance on outstanding loans at the bank is over $14,500. To test this at a significance level of 0.05, a random sample of n = 100 loan accounts is selected. Assuming that the population standard deviation is known to be $3,000, the value of that corresponds to the critical value is approximately $14,993.50.

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The critical value is the value that separates the rejection region from the non-rejection region. In this case, the critical value is $14,993.50. Since the sample mean is greater than the critical value, we reject the null hypothesis and conclude that the mean loan balance on outstanding loans at the bank is over $14,500.

The Loan Manager for State Bank and Trust Has Claimed