Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB 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)do not reject the null hypothesis
E)do nothing

Question

Quizplus · Accepted Answer

The null hypothesis is that the default rate on personal loans is no more than 5%, and the alternative hypothesis is that it is greater than 5%. We can set up a one-tailed test with a significance level of 0.10, and use the formula z = (p̂ - p) / √(p(1-p) / n) to calculate the test statistic, where p is the hypothesized proportion (0.05), p̂ is the sample proportion (30/500 = 0.06), and n is the sample size (500).

Plugging in the values, we get z = (0.06 - 0.05) / √(0.05(1-0.05) / 500) = 1.41. The critical value for a one-tailed test at a significance level of 0.10 is 1.28. Since our test statistic (1.41) is greater than the critical value (1.28), we can reject the null hypothesis and conclude that the default rate on personal loans is greater than 5%. Therefore, the appropriate decision is to not reject the null hypothesis.

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks α\alphaα

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks $\alpha$