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11. A test of the claim μ ≠ 68 is conducted. If we rejected the null hypothesis using a small sample of data, should we have a concern about the validity of our conclusion since the test relied on a small sample of data? What if we had narrowly failed to reject the null hypothesis when using a small sample size? Is there more cause for concern when we fail to reject using a small sample of data?
A. There shouldn't be a concern over the small sample size when we are able to reject the null hypothesis; however, when we cannot reject the null hypothesis, it could be a result of the reduced power of a small sample hypothesis test.
B. There should be a concern over the small sample size when we are able to reject the null hypothesis; however, when we cannot reject the null hypothesis, it should not be a concern because the of the reduced power of a small sample hypothesis test.
C. The t-test is more powerful than the z-test, so in both cases we are less likely to commit an error when using a small sample instead of a larger sample.
D. The sample size is never an issue in a hypothesis test.
E. We need more information to answer.
A. There shouldn't be a concern over the small sample size when we are able to reject the null hypothesis; however, when we cannot reject the null hypothesis, it could be a result of the reduced power of a small sample hypothesis test.