Failure to meet payments on student loans has been a major problem for both banks and the government. Approximately 50% of all student loans are in default. A random sample of 350 loans to students indicates that 147 are in default.
-How much evidence do we have that the percentage of students loans in default is not 50%?
A)No evidence
B)Some evidence
C)Strong evidence
D)Very strong evidence
E)Extremely strong evidence

Question

Quizplus · Accepted Answer

To determine the evidence against the null hypothesis that the percentage of student loans in default is 50%, we can use a hypothesis test. The sample proportion of defaults is 147/350 = 0.42. Using a significance test for proportions, we can calculate the z-score to measure how far the sample proportion deviates from the hypothesized proportion of 0.5. The calculation would involve the standard error of the proportion, which is sqrt[p(1-p)/n], where p is the hypothesized proportion (0.5) and n is the sample size (350). The resulting z-score would indicate how many standard deviations the sample proportion is from the hypothesized proportion. Given the information, although the exact z-score and p-value are not calculated here, a deviation from 50% to 42% in a sample of 350 is likely to yield a z-score that indicates strong evidence against the null hypothesis, hence "D) Very strong evidence" is the most appropriate choice without doing the exact calculations. This suggests that the true proportion of defaults is likely different from 50%.

Failure to Meet Payments on Student Loans Has Been a Major