A school teacher of a business course boasts that his students is so smart and that the average time they spent on reading books is more than 80 minutes per day. Suppose that the amount of time students spend daily reading books is normally distributed with a standard deviation of 15 minutes. A random sample of 30 students was drawn, and each reported the amount of time spent on reading books (in minutes). The sample mean was found to be 72 minutes.

a. Can we infer at the 10% significance level that the population mean is more than 90 minutes?

b. Determine the 90% confidence interval estimate of the population mean?