Question

Circle the best answer. The choice between a z-test and a t-test for a population mean depends primarily on: a. the sample size. b. the level of significance. c. whether a one- or two-tailed test is indicated. d. whether the given standard deviation is from the population or the sample. e. a z-test should never be used.

Answer 1

Correct option is (d).

Explanation:

A hypothesis test for single mean can be used to determine the significance of the claimed value of the population mean μ.

Now there are two test for mean:

• z-test
• t-test

A z-test is used when it is provided that the population is normally distributed, the sample is large and the population standard deviation value is provided.

A t-test is used when it is assumed that the population is normally distributed, the sample is large enough and the population standard deviation is not known.

So, in case there is no information about the population standard deviation (σ) but the sample standard deviation is either given or can be calculated from the provided data set, then the hypothesis test for single mean can be performed using the t-test.

Hence, the choice between a z-test and a t-test for a population mean depends primarily on whether the given standard deviation is from the population or the sample.

Thus, the correct option is (d).