1. A hypothesis test for a population mean is to be performed.True or false: for

Question

1. A hypothesis test for a population mean is to be performed.True or false: for a fixed sample size, increasing the significancelevel will decrease the power of the test? A) True B) False 2. A hypothesis test for a population mean is to be performed.True or false: the further the true mean is from thenull-hypothesis mean, the greater the power of the test? A) True B) False 1. A hypothesis test for a population mean is to be performed.True or false: for a fixed sample size, increasing the significancelevel will decrease the power of the test? A) True B) False 2. A hypothesis test for a population mean is to be performed.True or false: the further the true mean is from thenull-hypothesis mean, the greater the power of the test? A) True B) False

Explanation / Answer

1. False. If you increase thesignificance level (for example, go from .01 to .05) you would makeit easier to reject the null hypothesis. If you fail to reject anincorrect null hypothesis (fail to accept atrue alternate hypothesis), that is a type II error. Theprobability of not commiting a type II error is the power of thetest, so if you increase the significance level, you would increasethe power. 2. True. If the true mean is faraway from the null hypothesis mean, we will reject the nullhypothesis more often. By rejecting the null hypothesis more often,we are decreasing the probability of failing to reject the nullhypothesis, which, if the null hypothesis wereactualy correct, would be a type II error. So the probability of atype II erro is decreased, so the power increases. *Tip for dealing with increasing power: The easier it is toreject the null hypothesis, the lesser the probability of a type IIerror, meaning greater power. Theoretically, even though this issilly, if we rejected the null hypothesis every single time,automatically, the power would be 100% because we would never failto reject an incorrect null (probability of Type II error would be0%). Of course, there would be no statistical purpose for such apractice, but it helps in figuring out these types ofproblems.

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