Question

a) Suppose we were not sure if the distribution of a population was normal. In which of the following circumstances would we NOT be safe using a t procedure?

A. A histogram of the data shows moderate skewness.
B. The mean and median of the data are nearly equal.
C. A stemplot of the data has a large outlier.
D. The sample standard deviation is large.

(b) Which of the following is an example of a matched pairs design?

A. A teacher compares the pre-test and post-test scores of students.
B. A teacher calculates the average scores of students on a pair of tests and wishes to see if this average is larger than 80%.
C. A teacher compares the scores of students using a computer based method of instruction with scores of other students using a traditional method of instruction.
D. A teacher compares the scores of students in her class on a standardized test with the national average score.

(c) You are thinking of using a t procedure to test hypotheses about the mean of a population using a significance level of 0.05. You suspect the distribution of the population is not normal and may be moderately skewed. Which of the following statements is correct?

A. You may use the t procedure, but you should probably only claim the significance level is 0.10.
B. You may not use the t procedure.  t procedures are robust to nonnormality for confidence intervals but not for tests of hypotheses.
C. You may use the t procedure, provided your sample size is large, say at least fifty.  
D. You should not use the t procedure because the population does not have a normal distribution.

Answer 1

a. Due to outlier the normality get disturbed

So answer here is

C. A stemplot of the data has a large outlier.
b. A matched pairs design is a special case of a randomized block design. It can be used when the experiment has only two treatment conditions; and subjects can be grouped into pairs, based on some blocking variable. Then, within each pair, subjects are randomly assigned to different treatments.

So answer here is A. A teacher compares the pre-test and post-test scores of students.

c. For using t distribution normality assumption is must

D. You should not use the t procedure because the population does not have a normal distribution.