The mean drying time of certain paint in a certain application is known to be 12

Question

The mean drying time of certain paint in a certain application is known to be 12 minutes. A new additive will be tested to see if it reduces drying time. Fifty specimens will be painted with the new paint. Let be the mean drying time for the new paint. The investigators wish to test H0: 12 vs HA: <12 at =0.05. Suppose that the population standard deviation of drying times is =2 minutes and the true mean drying time of the new paint is 11.5 minutes. A. For the test with significance level 0.05 and 0.1, which one would have higher power? B. Ifthetruestandarddeviationwaslarger(>2),wouldthepowerbe higher or lower (as compared to the original scenario)? C. Ifthesamplesizewaslarger(n>50),wouldthepowerbehigherorlower (as compared to the original scenario)? D. If the true mean drying time of the paint was 11 minutes, would the power be higher or lower (as compared to the original scenario)?

Explanation / Answer

A. For the test with significance level 0.05 and 0.1, which one would have higher power?

hihger power will be 0.05

B. Ifthetruestandarddeviationwaslarger(>2),wouldthepowerbe higher or lower (as compared to the original scenario)?

awould be lower

C. Ifthesamplesizewaslarger(n>50),wouldthepowerbehigherorlower (as compared to the original scenario)?

would be higher

D. If the true mean drying time of the paint was 11 minutes, would the power be higher or lower (as compared to the original scenario)?

would be lower

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