2. (10 points) Consider the following frequency table of observations on the random variable X. Values 2 4 or more Observed 4 frequency 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 H. : J, = H, against H,: u, # u,. Suppose that sample sizes n, = 10 and n, = 10, that =7.8, and =5.6, and that =4, and =9. Assume that and that the data are drawn from normal distributions. Use a = 0.05. Test the hypothesis and find the P-value.1. An article in the AS CE 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 (0C) 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 H: u 75 22.5, using a = 0.05. Find the P-value. b. (5 points) Check the assumption that interior temperature is normally distributed. 5. A random sample of 500 adult residents of Maricopa County indicated that 385 were in favor of increasing the highway,r speed limit to 75 mph, and another sample of 400 adult residents of Pima County indicated that 267 were in favor of the increased speed limit. a. (5 points) Do these data indicate that there is a difference in the support for increasing the speed limit for the residents of the two counties? Use a = 0.05. What is the P-value for this test? 13. Suppose that and . With the sample sizes given here, what is the power of the test for this two-sided alternate? 0. Suppose that and . Determine the sample size needed to detect this difference with a probability of at least 0.9. 4. {10 points) A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers who are familiar with both languages are asked to code a standard function in both languages and the time (in minutes) is recorded. The data follow: Programm Design Design er Language 1 Language 2 __ ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ Find a 95% confidence interval on the difference in mean coding times. Is there any indication that one design language is preferable