MAT 124 – Exam 3 NAME:Each problem is worth 10 points. Please show all the steps for computing the confidence intervals and for running a hypothesis test.1. A random sample of 82 Freshman students at RWU were interviewed and 65 students said they would recommend a country music artist perform at the spring concert. Let p represent the population proportion of all Freshman students who would recommend that a country music artist perform at the spring concert. Find and interpret a 95% confidence interval for p.2. A pizza restaurant advertises that delivery will be no more than 30 minutes. A random sample of 14 delivery times has a sample mean x=35 .57 minutes and standard deviation s=5.88 minutes. Based on this sample, test the hypothesis that the delivery time greater than 30 minutes. Use a 5% level of significance.3. A recent study looked at the average number of miles per week that a pizza delivery driver put on his or her car over the past 9 weeks. The sample data showed that 𝑥 = 150 miles and s = 30 miles. Find and interpret the 95% confidence interval for the population mean number of miles driven?4. Female athletes at the University of Colorado Boulder have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 female athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of female athletes who graduate from this University is now less than 67%? Use a 5% level of