b. (5 points) Check the assumption that interior temperature is normally distributed.An article in the A503 Joumm' of Energy Engineering {1999, Vol. 125, pp. 5975] describes a stud!\"I ofthe thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures [T] reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. a. [5 points] Test the hypotheses Hg: p = 22.5 versus H1: p at 22.5, using a = [1.05. Find the P value. 2. (10 points] Consider the following frequency table of observations on the random va riable X. Values Observed frequency Based on these 10E:I observations, is a Poisson distribution with a mean of 1.2 an appropriate model? Perform a goodnessoffit procedure with a = 0:35. Calculate the Pvalue for this test. [5 points] Consider the hypothesis test Ha : p1 = pg against H1: H1 at L12. Suppose that sample sizes m = 10 and n: = 10, that 3:71:18, and f2=5.6, and that 33:4, and 33:9. Assume that 012 = (122 and that the data are drawn from normal distributions. Use a = 0.05. Test the hypothesis and find the Pualue