A researcher developing scanners to search for hidden weapons at airports has co

Question

A researcher developing scanners to search for hidden weapons at airports has concluded that a new scanner is not significantly better than the current scanner. He made his decision based on a test using = 0.025. Would he have made the same decision at =0.20? How about  =0.001? Explain.

A. His decision may have been different for both o 0.001 and o 0.20. B. His decision would have been the same for both o 0.001 and a 0.20. C. His decision may have been different for 0.20 but would have been the same for o 0.001. D. His decision may have been different for o 0.001 but would have been the same for 0.20.

Explanation / Answer

Option D .

As null hypothesis are always significantly same i.e new scanner and current scanner are significantly same and alternative hypothesis will be not significantly same

The conclusion was new scanner was not significantly better than currrent scanner that means the null hypothesis got rejected i.e the test test statistic is smaller than = 0.025 thus the null hypothesis got rejected.

So the test statistic will also be smaller = 0.20 as = 0.20 > = 0.025 and decision will be same.

But if we decrease more it is not necessary that test statistic will be smaller than . i.e it is not necessary that test statistic will be smaller than = 0.001.

Therefore decision will be different at = 0.001 and same for = 0.20

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