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 alpha equals 0.025 .α=0.025. Would he have made the same decision at alpha equals 0.20 question mark α=0.20? How about alpha equals 0.005 question mark α=0.005? Explain.

Answer 1

Answer:

$\alpha=0.2$ we can't conclude if we reject or not the null hypothesis. Since the p value is higher than 0.025 but we don't know if it's less than 0.2 or higher than 0.2.

$\alpha=0.025$ FAIL to reject the null hypothesis. The new scanner is not significantly better than the current scanner

Step-by-step explanation:

At the begin we have a decision at $\alpha=0.025$. And the decision was: The new device is NOT significantly better than the current scanner. And on this case that represent FAIL to reject the null hypothesis.  

We FAIL to reject the null hypothesis when the p value is higher than the significance level, so then we have this:

$p_v >0.025$

For a significance level of $\alpha=0.2$ we have that:

$0.2>0.025$ and we know that $p_v >0.025$ and we can express this like this $0.025<p_v$. but we don't know if the p value is large enough to be higher than 0.2, so on this case we can't conclude if we reject or not the null hypothesis.

At the significance level of $\alpha =0.005$ we know that $0.005<0.025$ and we know that $p_v >0.025$ so then needs to be $p_v>0.005$ and we will have the same decision like at $\alpha=0.025$ FAIL to reject the null hypothesis.