As part of a study of informal financial markets in developing countries, you are investigating whether moneylenders charge "usurious" interest rates. you take a random sample of 61 loans made by moneylenders to farmers, for seeds and fertilizer. the sample mean interest rate is 37.4 (percentage points), and the sample variance is 16.8 (squared percentage points). farmers who are able to obtain bank loans for seeds and fertilizer pay 35.9 percentage points.
preliminary analysis shows it is reasonable to assume that interest rates charged by moneylenders on loans for seeds and fertilizer are approximately normally distributed. test the null hypothesis that the mean interest rate charged by moneylenders is no greater than 35.9 percent, against the alternative that it is greater. give the test statistic and rejection region, as well as the conclusion of the test. use a 5% level of significance.
assume there is no difference between the creditworthiness of farmers who get bank loans for seeds and fertilizer and those who borrow from moneylenders. otherwise, this hypothesis test would not make sense, because any observed difference in interest rates then could be due to a difference in the riskiness of the loans.
before conducting this hypothesis test using the rejection region approach, let’s conduct it using the p-value approach.
1. what is the p-value? use 4 decimals for your answer.
2. now taking the rejection region approach, what is the critical value? use 2 decimals for your answer.