Chapter 21, Problem 5E

To determine

To explain would you have made the same decision at $\alpha =0.10$ and how about $\alpha =0.01$ .

Answer to Problem 5E

Yes, the same decision at $\alpha =0.10$ but not at $\alpha =0.01$ .

Explanation of Solution

It is given in the question that a researcher developing scanners to search for hidden at airports has concluded that a new device is significantly better than the current scanner. He made this decision based on a test using $\alpha =0.05$ . Thus, yes, we would have made the same decision at $\alpha =0.10$ because P-value must have been less than $0.05$ to have allowed for the null to be rejected, so it must also be less than $0.10$ . And we have not necessarily made the same decision at $\alpha =0.01$ because the p-value must also be less than $0.01$ for us to reject the null hypothesis and reach the same conclusion in this case.