For each statement, determine it is true or false. (a) If the sample size is dec

Question

For each statement, determine it is true or false. (a) If the sample size is decreased when testing a hypothesis, the power would be expected to increase. (b) If the significance level of a test is decreased, the power would be expected to increase. (c) If a test is rejected at the significance level , the probability that the null hypothesis is true equals . (d) The probability that the null hypothesis is falsely rejected is equal to the power of the test. (e) A type I error occurs when the test statistic falls in the rejection region of the test. (f) In testing a hypothesis, when the difference between the hypothesized mean and the actual mean (shift from µ0 to µa) is increased, the power of the test will decrease. (g) In testing a hypothesis, when the standard deviation is decreased, the power of the test will decrease. (h) The likelihood ratio is a random variable.

Explanation / Answer

(a) If the sample size is decreased when testing a hypothesis, the power would be expected to increase.
No, It increase the chance to increase the Type I Error, it implies decrease in the Power of test

(c) If a test is rejected at the significance level a, the probability that the null hypothesis is true equals a.
true, Type I error explains Reject Ho, when Ho is True. By the defination it explains the null hypothesis is true equals a

(d) The probability that the null hypothesis is falsely rejected is equal to the power of the test.
true, The power of a hypothesis test is the probability of making the correct decision if the alternative hypothesis is true

(e) A type I error occurs when the test statistic falls in the rejection region of the test.
True, It occurs when it resides in side the rejection area

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