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A. (10 points, 25 minutes) A firm's manager wishes to determine if the probability that employees visit the firm's medical consulting room is the same for every working day in the week. Based on a random sample of four complete working weeks, we have obtained the following information: Weekday Number of visits to the medical consulting room Monday 49 Tuesday 35 Wednesday Thursday 39 Friday 15 At the 5% significance level, what would the firm's manager conclusion be about his/her initial hypothesis? B. (10 points, 25 minutes) It is known that the expense in computer equipment for firms having less than 250 employees is a normally distributed r.v. X. In order to estimate the mean expense, a r.s. of size n = 15 is taken, providing a mean expense of 6000 euros, and a standard deviation of 7500 euros, i) Based on the distribution of X, obtain, providing all relevant details, the theoretical expression for the 1 -a confidence interval for the population mean expense, m, to be applied in this specific case. ii) Using the information provided in this exercise, compute the 95% confidence interval for the population mean expense. ") At the 5% confidence level, test the null hypothesis Ho : m = 10000 against alternative hypothesis H1 :m # 10000. C. (10 points, 25 minutes) Let X be a r.v. having a y(o, 3) distribution; that is, with probability density function: 120, 4 20 We wish to test the null hypothesis Ho : a = - against the alternative hypothesis #1 : a = 2. In order do so, a random sample of size n = 1, X, is taken. 1) Obtain the form of the most powerful critical region for this test. ii) Under the null hypothesis, what is the distribution of the test statistic X7 Hi) At the 5% significance level, provide the specific most powerful critical region for this test. - 0.6