If samples are drawn from a population that is normal,a goodness-of-fit test for normality could yield
A)Type I error but not Type II error.
B)Type II error but not Type I error.
C)either Type I error or Type II error.
D)both Type I and Type II errors.

Question

Quizplus · Accepted Answer

A goodness-of-fit test for normality is designed to test whether a sample comes from a normally distributed population. If the population is indeed normal, the test should not result in a rejection of the null hypothesis. However, with any statistical test, there is always the possibility of making a Type I or Type II error. In this case, a Type I error would occur if we reject the null hypothesis (i.e. conclude that the population is not normal) when it is actually true. This means we would be incorrectly concluding that the sample came from a non-normal population. On the other hand, a Type II error would occur if we fail to reject the null hypothesis (i.e. conclude that the population is normal) when it is actually false. This means we would be incorrectly concluding that the sample came from a normal population, even though it did not. Since the question asks what kind of errors could be made, answer A is correct, as a goodness-of-fit test for normality could result in a Type I error but not a Type II error.

If Samples Are Drawn from a Population That Is Normal,a