Question

We have a right tail test for a population mean. The sample size is 32. Assume the null hypothesis is true. Which test statistic value gives a Type I error for a significance level of 5% and a correct decision for a significance level of 2

Answer 1

The test statistic value that gives a Type I error for a significance level of 5% and a correct decision for a significance level of 2% in a right-tail test with a sample size of 32 is any value greater than 2.326.

Step-by-step explanation:

Since this is a right-tail test, we compute the p-value as the area to the right tail of the z-test in a standard normal distribution.

Given a significance level of 5%, the critical z-value is approximately 1.645. For a significance level of 2%, the critical z-value is approximately 2.326.

To ensure a correct decision at the 2% significance level, we need the test statistic value to be greater than 2.326.

Any test statistic value greater than 2.326 would result in a Type I error for a significance level of 5% and a correct decision for a significance level of 2%.