Question

You would like to estimate the mean price of milk (per gallon) in your city. You select a random sample of prices from different stores. The sample has a mean of

3.60 dollars and a standard deviation of 0.22 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, and t refers to a variable having a t distribution.)

Sampling Scenario	Z	t	could use either Z or t	unclear
(1) The sample has size 17, and it is from a population with a distribution about which we know very little.
(2) The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 0.26.
(3) The sample has size 20, and it is from a normally distributed population with unknown standard deviation.
(4) The sample has size 110, and it is from a non-normally distributed population.
(5) The sample has size 11, and it is from a normally distributed population with a known standard deviation of 0.26.

Answer 1

Sampling Scenario Z t could use either Z or t unclear (1) The sample has size 17, and it is from a population with a distribution about which we know very little. unclear (because population distribution is unknown , also, sample size is small (2) The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 0.26. Z (because σ is known) (3) The sample has size 20, and it is from a normally distributed population with unknown standard deviation. t (because σ is unknown) (4) The sample has size 110, and it is from a non-normally distributed population. could use either Z or t (5) The sample has size 11, and it is from a normally distributed population with a known standard deviation of 0.26. Z