You would like to construct a 95% confidence interval to estimate the population mean annual income for people over age 40 in your state. You choose a random sample of such incomes and compute the mean of the sample as 40,742.5 dollars with a standard deviation of 7584.1 dollars. (a) What is the best point estimate, based on the sample, to use for the population mean? dollars (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% confidence interval for the population mean. (In the table, Z refers to a standard normal distribution, and refers to a t distribution.) Sampling scenario The sample has size 17, and it is from a normally distributed population with an unknown standard deviation. The sample has size 75, and it is from a non-normally distributed population with a known standard deviation of 7575. The sample has size 10, and it is from a population with a distribution about which we know you little ZI O O O Could use either Z or / Unclear O O X X 5

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