A company, MM, selling items online wants to compare the transport times for two transport firms for delivery of the goods. To compare the two companies recordings of delivery times on a specific route were made, with a sample size of n = 9 for each firm. The following data were found: Firm A: JA = 1.93 d and SA = 0.45 d, Firm B: B = 1.49 d and sg = 0.58 d. note that d is the SI unit for days. It is assumed that data can be regarded as stemming from normal distributions. a) We want to test the following hypothesis Ho: MAHB H A #MB = 5% What is the p-value, interpretation and conclusion for this test (at a = ! level)? b) Find the 95% confidence interval for the mean difference A - MB. c) What is the power of a study with n = 9 observations in each of the two samples of detecting a potential mean difference of 0.4 between the firms (assume that = 0.5 and that we use a = 0.05)? d) What effect size (mean difference) could be detected with n = 9 observa- tions in each of the two samples with a power of 0.8 (assume that = 0.5 and that we use a = 0.05)? e) How large a sample size (from each firm) would be needed in a new inves- tigation, if we want to detect a potential mean difference of 0.4 between the firms with probability 0.90, that is with power=0.90 (assume that = 0.5 and that we use a = 0.05)?