) Suppose a coin is to be tossed n times for the purpose of estimating T, whereP(heads).T = i. State the approximate sampling distribution of P, i.e. the sample proportion,and

briefly state the condition on n which should be satisfied for the approximation to be reasonable.l..) ii. How large must n be to guarantee that the width of the 99% confidence interval for T will be less than 0.02? (b) A company wants to check the quality of its customer service regarding web chat enquiries. For this reason the manager wants to compare the waiting times until each enquiry was answered during the years 2018 and 2019. Unfortunately, extensive records of the company are not available, and only random samples of web chat enquiries within these two years are available. The data, measured in minutes of waiting times, are provided below for each year. i. Use an appropriate hypothesis test to determine whether the mean waiting times,were different between these two years. Test at two appropriate significance levels, stating clearly the hypotheses, the test statistic and its distribution under the null hypothesis. Comment on your findings. ii. State clearly any assumptions you made in i. (2 marks)iii. Adjust the procedure above in i. to determine whether the mean waiting time in2019 was less than that in 2018.