The questions are attached

J. \\ ; J. L) Problem 1 . There were 1200 students in a large Introductory Statistics course last semester. A questionnaire was sent by email to a simple random sample of 120 of them asking them the amount of money per week they spent on enter- tainment. Suppose that 36 students| responded and 84 did not respond. A simple random sample of 24 students were selected from 84 non-respondents and intensive efforts such as phone call and email with monetary award were made to obtain responses from 24 students. The results are summarized in the following table: Students returning questionnare Students responding to intensive efforts Sample size 36 24 Sample mean $28.2 $14.8 Sample Sd. $4.8 $3.2 o (a) Estimate the average amount of money the students spent on en tertainment . o (b) Estimate the variance of the estimator in part (a). Problem 2. This semester there are 1000 students in the large Introductory Statistics course mentioned in the problem 1 and a similar survey will be conducted this semester. Given that the cost of the processing a questionnaire is $1.8 and the cost of obtaining and processing the data for each student to the intensive effort is $5.0 (ca : 0). How man}r questionnaires should be sent out in the rst phase and how many non-respondents should be sampled in the second phase if we want the standard deviation of the resulting estimator to be approximately 1? ( It is given that the standard deviation of the population can be estimated to be 7.2 )