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. Ophelia's null hypothesis is ___.
A) π 0.05
B) π = 0.05
C) n = 30
D) n = 500
E) n = 0.05

Question

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. Ophelia's null hypothesis is ___.
A) π > 0.05
B) π = 0.05
C) n = 30
D) n = 500
E) n = 0.05

Quizplus · Accepted Answer

The null hypothesis is a statement that assumes there is no difference or relationship between the variables being tested. In this case, the null hypothesis would be that the default rate on personal loans is equal to or less than 5%, represented symbolically as π <= 0.05. However, since the question is asking for Ophelia's null hypothesis, which is the opposite of the research hypothesis, the answer is π > 0.05. This means that Ophelia assumes that more than 5% of personal loans are in default, and any difference in the sample data would be due to chance.