For each of the following statements, state whether the statement is true or fal
ID: 3130722 • Letter: F
Question
For each of the following statements, state whether the statement is true or false, and justify your answer: (a) The significance level of a hypothesis test is equal to the probability that the null hypothesis is true. (b) If the significance level of a hypothesis test is decreased, the power would be expected to increase. (c) If a null hypothesis is rejected at the significance level of , the probability that the null hypothesis is true equals . (d) A type I error occurs when the test statistic falls in the rejection region of the test. iid N(0,1) N(5,9) iid 2 (4) (e) If the p-value is 0.03, the corresponding test will fail to reject the null hypoth- esis at the significance level of 0.02. (f) If the null hypothesis is true, the probability of a type II error is zero. (g) The p-value of a hypothesis test is the probability that the null hypothesis is correct. (h) If a test rejects the null hypothesis at a significance level of 0.06, then the p-value is less than or equal to 0.06.
Explanation / Answer
(a) The significance level of a hypothesis test is equal to the probability that the null hypothesis is true.
FALSE. We do not assign a probability that Ho is true. It is just true or false on its own.
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(b) If the significance level of a hypothesis test is decreased, the power would be expected to increase.
FALSE. The power decreases as well. [ANSWER]
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(c) If a null hypothesis is rejected at the significance level of , the probability that the null hypothesis is true equals .
TRUE. [ANSWER]
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(d) A type I error occurs when the test statistic falls in the rejection region of the test.
FALSE. Not automatically. If we reject Ho, a type error might occur, but not always.
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