Q3 Select the TWO options that are TRUE statements about two

Q3

Select the TWO options that are TRUE statements about two-sample t-tests.

Select one or more:

A) The same formula is used for the ESE (estimated standard error) in the two-sample t-test with a common variance and the two-sample z-test.

B) The critical values for the two-sample t-test with unequal variances and the two-sample z-test, for given sample sizes, are generally different.

C) A researcher has collected two samples of data and the sample variances are 1.45 and 2.11. It wouldnot be appropriate to use the two-sample t-test with a common variance.

D) A researcher has collected two samples of data and the sample variances are 2.16

Solution

The following are the true statements:

B) The critical values for the two-sample t-test with unequal variances and the two-sample z-test, for given sample sizes, are generally different.

D) A researcher has collected two samples of data and the sample variances are 2.16² and 4.82². It would not be appropriate to use the two-sample t-test with a common variance.

Reason: The sample standard deviations are different, so the variances will be different.