Question 3 20 marks Answer this question using the following information: R -"'"' q uni-Ill\" PG) 1 Z

Question 3 Answer this question using the following information: < z < 1.53) = 0.4370 < z < 2.17) = 0.4850, where Z is the standard normal random variable. 20 marks An educator wishes to estimate the population mean of the time spent per week by secondary students on doing physical exercises during this period of online teaching. (a) (b) The educator has selected a preliminary random sample of 40 secondary students and found that they spent a total of (2 x R + 150) hours on doing physical exercises during the week of study. Find the best point estimate for the population mean. Correct your answers to 2 decimal places. (4 marks) The educator has then taken another random sample of 100 secondary school students to estimate the population mean. Based on this sample, the mean and standard deviation of the time spent were (0.1 x R + 3.5) hours and 1.1 hours respectively. Find the 87.4% confidence interval of the population mean. Correct your answers to 2 decimal places. (8 marks) (ii) (iii) Find the maximum error of the estimate at 87.4% confidence. Correct your answers to 2 decimal places. (4 marks) Suppose the educator plans to carry out the study again with a new sample. Find the minimum sample size if the educator wants to be 97% confident that the estimated population mean has a maximum error of 0.05 + (4 marks)