We want to conduct a hypothesis test of the claim that the population mean score on a nationwide examination in biology is different from 479

Question

We want to conduct a hypothesis test of the claim that the population mean score on a nationwide examination in biology is different from 479

. So, we choose a random sample of exam scores. The sample has a mean of 484

and a standard deviation of 78

For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places.

(a) The sample has size 19

, and it is from a normally distributed population with an unknown standard deviation.

z =

t =

It is unclear which test statistic to use.

b) the sample has size 110, and it is from a non-normally distributed population with a known standard deviation of 78

.

z =

t =

It is unclear which test statistic to use.

Answer 1

When the standard deviation is known, you use the z statistic. When the standard deviation is unknown, you use the t statistic.