Q. 9 A market researcher wishes to examine the effectiveness of a advertising campaign directed at college students for a new line of shoes. Before the campaign starts she interviews a sample of 400 students and asks them if they knew about the new line of shoes and 47 did. When the campaign had been running for two weeks, she took another sample of 500 students (independently of the first sample) and this time 88 had heard of the shoes. a) State the null and alternative hypotheses of interest to the market researcher. b) Carry out the test, find the p-value and report your conclusions at the 5% level of significance. c) Construct a 99% confidence interval for the difference in proportions of students know- ing about the shoes before and after the campaign