Quiz #8

Answers are given in the answer boxes below. Scroll down for explantions for the answers (given in red).

Be sure to put your name on this quiz. Write True or False in each of the answer boxes below (as opposed to just putting T or F.).

answer
Statement 1 True
Statement 2 True
Statement 3 True
Statement 4 True
Statement 5 True

Indicate if the following statements are true or false by placing the word True or False in the proper answer boxes above.

For all of the statements, consider that the situation is that one has observations of iid random variables from a continuous distribution.
Statement 1
The signed-rank test is valid for testing hypotheses about the means of symmetric distributions.
Statement 2
The signed-rank test is valid for testing hypotheses about the medians of symmetric distributions.
Statement 3
The sign test is valid for testing hypotheses about the means of symmetric distributions.
Statement 4
The sign test is valid for testing hypotheses about the medians of symmetric distributions.
Statement 5
The sign test is valid for testing hypotheses about the medians of skewed distributions.
The sign test is valid for tests about the median, whether the distibution is skewed or symmetric. So 4 and 5 are true. If the distribution is symmetric, the mean will be the same as the median, and so with a symmetric distribution we can consider the sign test to be valid for tests about the mean. So 3 is true. With a skewed distribution, the signed-rank test isn't guaranteed to behave decently as a test about the mean or the median, but with a symmetric distribution it's valid for tests about the mean/median. So 1 and 2 are true. (Note: Both the sign test and the signed-rank test are also valid for testing the null hypothesis of no treatment effect against the general alternative when one is working with matched pairs differences.)