A class survey in a large class for first-year college students

     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?