Quiz #6
The answer is given in the answer box below.
Scroll down for an explantion for the answer (given in red).
Be sure to put your name on this quiz. Write the letter corresponding
to the correct answer in the answer box below.
Which of the following statements is not true concerning the
power of Welch's test to reject the null hypotheis of equal means in
favor of the alternative that the means are not equal?
(Choose the answer from the choices given below and write the
appropriate letter in the answer box above. (All but one statement is
true.)
- [ A ] It's risky to use a table, like the one in the appendix of
the text by Samuels and Witmer, to determine the minimum sample sizes
needed to achieve a certain power, and then use these sample sizes,
because larger sample sizes may be needed for the test to be
(approximately) valid if nonnormality exists.
- [ B ] Keeping everything else fixed, the power can be increased by
decreasing the size (level) of the test. (To think about: If the
rejection region is altered to decrease the possibility of a type I
error if the null hypothesis is true, should more rejections occur, or fewer
rejections occur, if the alternative hypothesis is true?)
- [ C ] Keeping everything else fixed, the power can be increased by
increasing the sample sizes.
- It is risky to rely on the table in the appendix --- the table
may indicate sample sizes that are okay if the distributions are
approximately normal, but are inadequate to even yield a valid result if the
distributions are nonnormal. So [ A ] is true.
- [ B ] is false. If the size of the test is decreased, values are
removed from the rejection region (the boundary for the rejection region
is moved "farther out"), making it less likely to reject, whether the
null hypothesis is true or the alternative hypothesis is true. Since
the power is the probability of rejecting the null hypotheis if the
alternative is true, making it harder to reject will result in decreased
power.
- Adding more information (more data) will not hurt the performance
of the test --- it will improve the performance of the test.
(Increasing the sample sizes reduces the uncertainty, making it easier to
detect that the means are different if the alternative is true.)
So [ C ] is true.