Question

Suppose that we want to estimate the mean score on a nationwide examination in finance, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 514 and a standard deviation of 77. 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, refers to a variable having a standard normal distribution, and 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 110, and it is from a non-normally distributed population.
(3) The sample has size 10, and it is from a normally distributed population with unknown standard deviation.
(4) The sample has size 80, and it is from a non-normally distributed population with a known standard deviation of 75.
(5) The sample has size 13, and it is from a normally distributed population with a known standard deviation of 75.

Answer 1

1) The sample has size 17, and it is from a population .........                       Unclear

2) The sample has size 110, and it is from a non-normally ........................could use either Z or t

3) The sample has size 10, and it is from a normally ......................           t

4) The sample has size 80, and it is from a non-normally distributed ........z

5) The sample has size 13, and it is from a normally ..................................z