MULTIPLE CHOICE : For a hypothesis test with a fixed level of significance (), w

Question

MULTIPLE CHOICE:

For a hypothesis test with a fixed level of significance (), what will happen to the probability of a Type II error () if we decrease the sample size of the test?

a. type II error will increase

b. type II error will decrease

c.type II error will not change d. we cannot determine what will happen

1B. We have created a 96% confidence interval for and it is (83.6 to 91.4). What conclusion will we make if we test Ho: =84 vs. Ha: 84 at a level of significance of = .04?

a. fail to reject Ho

b. accept Ho as a true statement

c. reject Ho (Ha is more likely)

d. we are unable to tell what the result will be

Explanation / Answer

a) Decreasing sample size makes the hypothesis test less sensitive - less likely to reject the null hypothesis when it is, in fact, false. Thus, it decreases the power of the test. P(type 2 error) = 1 - power

Therefore it increases the probability of making type 2 error, when sample size is decreased

a. type II error will increase

b) Since 84 is within the interval, we cannot reject null hypothesis at 0.04 significance level

b. accept Ho as a true statement

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