1) A class survey in a large class for first-year college students asked, “About how many minutes do you study on a typical weeknight?” The mean response of the 269 students was x̄ = 137 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 65 minutes in the population of all first-year students at this university. a) Use the survey result to give a 99% confidence interval for the mean study time of all first-year students. b) What conditioned not yet mentioned must be met for your confidence interval to be valid? 2) There were actually 270 responses to the class survey in the above exercise. One student claimed to study 30,000 minutes per night. We know he’s joking, so we left this value out. If we did a calculation without looking at the data, we would get x̄ = 248 minutes for all 270 students. Now what is the 99% confidence interval for the population mean? (Continue to use σ = 65.) Compare the new interval with that from the exercise above. The message is clear: always look at your data, because outliers can greatly change your result. 3) The first exercise describes a class survey in which students claimed to study an average of x̄ = 137 minutes on a typical weeknight. Regard these students as an SRS from the population of all first-year students at this university. Does the study give good evidence that students claim to study more than 2 hours per night on average? a) State null and alternative hypotheses in terms of the mean study time in minutes for the population b) What is the value of the test statistic z? c) What is the P-value of the test? Can you conclude that students do claim to study more than two hours per weeknight on the average?