Question

t is hypothesized that​ 50% of Americans attend church regularly.​ Researchers, however, feel that this percentage is lower. In​ fact, they believe that​ 40% of Americans attend church regularly. Using​ 40% for the value in their alternative​ hypothesis, researchers conducted a study and found the power to be 0.95. Which of the following is the correct interpretation of this value of the power of the​ test?

Choose the correct answer below.

A.

If​ 40% of Americans really do attend church regularly like the researchers​ thought, then the probability of rejecting a null hypothesis that this percentage is​ 50% for the alternative that this percentage is less than​50% is 0.95.

B.

If​ 50% of Americans really do attend church​ regularly, then the probability the researchers would obtain a percentage of​ 40% is 0.95.

C.

If​ 50% of Americans really do attend church​ regularly, then the probability of rejecting a null hypothesis that this percentage is​ 40% for the alternative that this percentage is more than​ 40% is 0.95.

D.

If​ 40% of Americans really do attend church regularly like the researchers​ thought, then the probability of incorrectly rejecting the null hypothesis that this percentage is​ 50% is 0.95.

Answer 1

The power of the test is the probability of rejecting the null hypothesis, assuming that the true population proportion is equal to the critical parameter value. ... And the mean of all possible sample proportions is equal to the population proportion.

Answer is A)

If​ 40% of Americans really do attend church regularly like the researchers​ thought, then the probability of rejecting a null hypothesis that this percentage is​ 50% for the alternative that this percentage is less than​50% is 0.95.