[5] 1. In written assignment 6 we constructed a set of confidence intervals for the caffeine content of coffees. There were three questions on this topic, and for each question a different amount of information was provided to construct the interval. Let's revisit those intervals, but make use of what we now know about hypothesis testing. In the first case, the true (population) standard deviation of caffeine content in a large coffee was o = 25 mg. (Our sources also claimed the population mean was / = 100 mg, but we wanted to test that.) We collected a sample of 50 large coffees and recorded the following sample statistics: n = 50, i = 110 mg, s = 27 mg The resulting 95% confidence interval for the mean was: (103.07, 116.93) [1] a) Based on this scenario, define an appropriate null hypothesis and an appropriate alternative hypothesis for a statistical test to determine whether the mean caffeine content is 100 mg [1] b) State the appropriate conclusion of this hypothesis test using the data from this sample. (e.g. Do you reject the null hypothesis?). What did you base this conclusion on?[1] c) Would you expect the pvalue of this test to be above or below 0.05? Justify your answer. [2] d) Let 's now ignore this particular sample and examine the test process. Suppose the population mean caeine content was, in fact, 100 mg. If we were to repeat this process (of collecting a sample and constructing a hypothesis test based on a 95% condence interval) a. large number of times, for what proportion of tests would we expect to conclude that the mean is not 100 mg