Question;Chapters 7 and 8: 7.9, 7.10, 8.9, and 8.237.9 Suppose that we will take a random sample of size n from a population having mean u and standard deviation o. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean x: (note the x should have a line over it)a) u= 10, o= 2, n=25 c) u= 3, o=.1, n =4b) u= 500, o=.5, n=100 d) u= 100, o =1, n =1,6007.10 For each situation in Exercise 7.9, find an interval that contains (approximately or exactly) 99.73 percent of all the possible sample means. In which cases must we assume that the population is normally distributed? Why?8.9 The mean of the sample of 65 customer satisfaction ratings in Table 1.7 is 42.95. If we let u denote the mean of all possible customer satisfaction ratings for the XYZ Box video game system, and assume that the population standard deviation equals 2.64:a) Calculate 95 percent and 99 percent confidence intervals for u.b) Using the 95 percent confidence interval, can we be 95 percent confident that u is at least 42 (recall that a very satisfied customer gives a rating of at least 42)? Explain.c) Using the 99 percent confidence interval, can we be 99 percent confident that u is at least 42? Explain.d) Based on your answers to parts b and c, how convinced are you that the mean satisfaction rating is at least 42?8.23 The mean and the standard deviation of the sample of 100 bank customer waiting times in Table 1.8 are 5.46 and 2.475, respectively. Calculate a t- based 95 percent confidence interval for u, the mean of all possible bank customer waiting times using the new system. Are we 95 percent confident that u is less than six minutes?
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