Malls R Us developers is considering building a mall on the West side of East Overshoe,...

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Malls R Us developers is considering building a mall on the West side of East Overshoe, but they do not want to go forward if the mean household income in the area is too low to support their project. They will take a sample of incomes from the area and test (at the .05 level) to see if the mean income in the area is below $65,000 per year. They want to have at least a 90% chance of detecting the difference if the mean is actually $62,000 or less. Based on previous studies they believe the standard deviation for incomes is about $13,000. (a) Set up the test (parameter/variable/population.H0, Ha-just these) (no data yet collected - you can't actually carry out the test) (b) One team member suggests that they collect a (random) sample of 100 incomes for the study. If the mean income is $62,000, what is the probability that her test (with n = 100, using a = .05) will detect the difference? (does it reach .9 or greater?) (c) What is the smallest sample size that will give a <.05 and power at least .9 for true mean $62,000? Malls R Us developers is considering building a mall on the West side of East Overshoe, but they do not want to go forward if the mean household income in the area is too low to support their project. They will take a sample of incomes from the area and test (at the .05 level) to see if the mean income in the area is below $65,000 per year. They want to have at least a 90% chance of detecting the difference if the mean is actually $62,000 or less. Based on previous studies they believe the standard deviation for incomes is about $13,000. (a) Set up the test (parameter/variable/population.H0, Ha-just these) (no data yet collected - you can't actually carry out the test) (b) One team member suggests that they collect a (random) sample of 100 incomes for the study. If the mean income is $62,000, what is the probability that her test (with n = 100, using a = .05) will detect the difference? (does it reach .9 or greater?) (c) What is the smallest sample size that will give a <.05 and power at least .9 for true mean $62,000?