Suppose that you want to estimate the mean annual income for people over age40

in your state. You choose a random sample of such incomes and compute the mean of the sample as40179.5

dollars with a standard deviation of7632.8

dollars. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.

(In the table,

Z

refers to a variable having a standard normal distribution, andt

refers to a variable having atdistribution.)

Sampling ScenarioZtcould use either Z or tunclear(1) The sample has size 80, and it is from a non-normally distributed population with a known standard deviation of 7517.

(2) The sample has size 100, and it is from a non-normally distributed population.

(3) The sample has size 11, and it is from a population with a distribution about which we know very little.

(4) The sample has size 19, and it is from a normally distributed population with unknown standard deviation.

(5) The sample has size 15, and it is from a normally distributed population with a known standard deviation of 7517.