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Question 2 In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company wants to perform a test to determine whether this average duration of long- distance calls has changed. Fifty calls, originating from the town, was randomly selected and the following summary minutes. Ex = 205 E(x - x)2 = 56.43 a) Calculate the sample mean, x. b) Calculate the sample standard deviation c) Using the p value approach at the 1% level of significance, test whether the mean duration of long-distance calls from the town had increased. d) Construct the 99% confidence interval for the population mean duration of the long-distance calls from the town. Question 3 A random sample of residents from various income brackets were asked their opinion on tax reform for the country of Guyana. The data so gathered were analyzed by a statistician and the results he obtained using MINITAB are shown below: Expected counts are printed below observed counts Low Middle High Total For 26 75 14 115 (30. 67) (51 . 11) (33.22) Against 60 95 105 260 (69.33) (115 .56) ( * * ) Neutral 34 30 11 75 (20) (33.33) (21 . 67) Total 200 130 450 Chi-sq = 0. 71 + 11 . 17 + 11 . 12 + * * * - 3 . 66 + 11 . 89 + 9.8 + 0. 33 + 5 .25 = 55 . 2 DF = ??, p-value =??? a) Carefully define the null and alternative hypotheses of the x2 test underlying the generation of the above table. b) Find the missing values "*', '**', '*', '??' and '???' c) What is the conclusion of this test? Give reasons for your