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 to _______.
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 default rate in the sample is 30/500 = 6%, which is above the 5% standard but without additional statistical analysis (e.g., calculating a p-value or confidence interval), we cannot determine if this deviation is statistically significant. The choice to "fail to reject the null hypothesis" typically means that we do not have sufficient evidence to conclude that the default rate significantly exceeds the standard. Without evidence of a significant deviation, the appropriate decision is to maintain the current approach, which includes continuing with the same sample size and monitoring procedures.

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

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