Question

If you use a 0.10 level of significance in a two-tail hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean equals 500 if you use the Z test

Answer 1

Our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.

Explanation:

The hypotheses would be;

Null hypothesis;H0: μ = 500

Alternative hypothesis;Ha: μ ≠ 500

Since it's two - tailed at 0.1 level of significance, then each tail will contain 5% or 0.05. From the z-table attached, the corresponding critical value of 0.05 is approximately 1.645 standard deviations from the mean.

Thus, our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.