Question

A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. He made this decision based on a test using a = 0.05. Would he have made the same decision at a = 0.10? How about a = 0.01? Explain.

Answer 1

He can make the same decision at a = 0.10, but he may not make the same decision at a = 0.01

Explanation:

In hypothesis tests, critical regions are ranges of the distributions where the values represent statistically significant results. Analysts define the size and location of the critical regions by specifying both the significance level (alpha) and whether the test is one-tailed or two-tailed.

As the significance level gets bigger, the range of the critical region increases.

Therefore significant results at lower significance levels are still significant at higher significance levels. Thus significant result at a=0.05 is always significant at a=0.10

But significant result at a=0.05 may not be significant at a=0.01 since critical region shrinks, therefore the result may not fall in the critical region at a=0.01