An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 5975) describes a study of the 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 (C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. a. (5 points) Test the hypotheses H0: u = 22.5 versus H1: u 1: 22.5, using a = 0.05. Find the P- value. b. (5 points) Check the assumption that interior temperature is normally distributed. 2. (10 points) Consider the following frequency table of observations on the random variable X. Values 0 1 2 3 4 or more Observed frequency 24 30 31 11 4 Based on these 100 observations, is a Poisson distribution with a mean of 1.2 an appropriate model? Perform a goodness-of-fit procedure with a = 0.05. Calculate the P-value for this test.3. (5 points) Consider the hypothesis test HQ=2 I41 = I42 against H1: H1 1: pg. Suppose that sample sizes n1 = 10 and n2 = 10, that f1=7.8, and f2=5.6, and that 512:4, and 522:9. Assume that 012 = 022 and that the data are drawn from normal distributions. Use a = 0.05. Test the hypothesis and find the P-value