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, ar.s. of size n= 15 is taken,...

Extracted text: 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, ar.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. 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 ii) iii) H1: m 6= 10000. Let X be a r.v. having a y(a, 3) distribution; that is, with probability density function: Ar; a) =ax'e , x >0, a >0 We wish to test the null hypothesis Ho :a =against the alternative hypothesis Hị : a = 2. In order to do so, a random sample of size n = 1, X, is taken. i) 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 X? iii) At the 5% significance level, provide the specific most powerful critical region for this test. – 0.6 – B.