Question 3 (13 marks) An owner of a travel agency would like to determine whether or not the mean age of the agency's customers is under 60. If so, the owner plans to alter the destination of the agency's special cruises and tours. A random sample of 64 customers was analyzed, resulting in the sample mean of ages equal 57.3 years and the sample standard deviation of ages equals 7.5 years. a) State the null and alternative hypotheses for this study using full sentences and using mathematical notation. (4 marks) b) What sample statistic would you use to test the null hypothesis? (1 mark) c) What test statistic would you use to test the null hypothesis? Explain why you would choose this one. (2 marks) d) Calculate the value of the observed test statistic. (1 mark) e) Find the p-value for the observed test statistic. (1 mark) f) Using the 5% significance level, state whether you can reject the null hypothesis. Explain what your finding means in the context of the problem. (2 marks) g) Obtain and interpret a 90% confidence interval for the true mean age of all customers of the travel agency. (2 marks)