Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday,the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using $\alpha$ = 0.10,the appropriate decision is _______.
A) reduce the sample size
B) increase the sample size
C) reject the null hypothesis
D) fail to reject the null hypothesis
E) do nothing

Question

Quizplus · Accepted Answer

The null hypothesis is that the proportion of defaulted loans is equal to or less than 5%. The alternative hypothesis is that the proportion of defaulted loans is greater than 5%.

Since the p-value (calculated using the one-tailed z-test) is greater than the significance level of 0.10 (0.1131 > 0.10), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the proportion of defaulted loans is greater than 5%. Therefore, Ophelia O'Brien should do nothing and continue to monitor the default rate on personal loans.

Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors α\alphaα

Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors $\alpha$