## Quiz #6

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.

Question 1 False
Question 2 False

#### Question 1

Indicate if the following statement is true or false by placing the word True or False in the proper answer box above.
If the sample sizes are small (say less than 30), then one needs for the parent distributions of the data to be (exactly) normal in order for the Welch's test and confidence interval method to be reasonably accurate.
The statement is false. If the sample sizes are in the 20s, and both distributions are only mildly nonnormal, the accuracy of the procedures is pretty good. (If both distributions are skewed in the same way, or are perhaps light-tailed and symmetric or nearly symmetric, the accuracy can be good even if the sample sizes are less than 20.) Exact normality is unreasonable to expect, and should not be considered to be required, even with smallish sample sizes (but at the same time, you cannot expect good results in all situations --- some types on nonnormality cause great problems, especially for small sample sizes).

#### Question 2

Indicate if the following statement is true or false by placing the word True or False in the proper answer box above.
With regard to Welch's test and confidence interval method, if the parent distributions of the two samples are skewed, it's better if they are skewed in opposite directions in order to have a cancellation of the bad effects due to skewness.
The statement is false. Because one sample mean is subtracted from the other in the numerator of Welch's statistic, the distributions have to be skewed in the same direction in order to benefit from a cancellation effect.