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An article in the ASCEJournoi'ofEnergy Engineering {1999, Vol. 125, pp. 5975) describes a study of the thermal inertia properties of autoclaved aerated concrete used as

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An article in the ASCEJournoi'ofEnergy 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 Ho: [.1 = 22.5 versus H1: p: 22.5, using a = 0.05. Find the P- value. b. (5 points) Check the assumption that interior temperature is normallv distributed. 2. (10 points} Consider the following frequencv table of observations on the random variable X. values \"III 4 or more 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__: in = u: against H1: m at p2. Suppose that sample sizes m = 10 and n; = 10, that 3E1=7.8, and 222:5.6, and that 512:4, and 522:9. Assume that of = 022 and that the data are drawn from normal distributions. Use a = 0.05. Test the hypothesis and find the P-value. 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: Design Language 1 Design Language 2 Find a 95% confidence interval on the difference in mean coding times. Is there any indication that one design language is preferable? 5. A random sample of 500 adult residents of Ma ricopa County indicated that 385 were in favor of increasing the highway 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 ct = 0.05. What is the Palm for this test?I b. Suppose that p1 = 0.75 and p2 = 0.65 . With the sample sizes given here, what is the power of the test for this two-sided alte rnate'iI c. Suppose that p1 = 0.75 and p2 = 0.65 . Determine the sample size needed to detect this difference with a probability of at least 0.9

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