Question

Smokers are commonly thought of as nervous people whose emotionality is at least partly caused by the stimulating effect tobacco has on the nervous system. Nesbitt (1972) conducted a study with 300 college students and concluded that smokers are less emotional than nonsmokers, that smokers are better able to tolerate the physiological effects of
anxiety, and that, over time, smokers become less emotional than nonsmokers.
Subjects of both genders were drawn from three different colleges and classified as smokers if they smoked any number of cigarettes on a regular basis. In one aspect of the experiment, all subjects were given the Activity Preference Questionnaire (APQ), a test designed to measure the emotionality of the subjects. The APQ is scored using an ordinal scale of 0–33, with lower scores indicating less emotionality, that is, greater sociopathy. The mean overall scores were 18.0 for smokers and 20.3 for nonsmokers.

Suppose this experiment is repeated using a group of 8 randomly chosen smokers and 10 randomly chosen nonsmokers. Do these data support the same conclusion concerning emotionality as Dr. Nesbitt’s data?

Smokers: 16, 18, 21, 14, 25, 24, 27, 12

Nonsmokers: 17, 15, 28, 31, 30, 26, 27, 20, 21, 19

*Nonparametric Statistical Inference, 5th edition, J. D. Gibbons and S. Chakraborti. (Chapter 8: Problem 8.10)

Answer 1

> smoker=c(16,18,21,14,25,24,27,12)
> nonsmokers=c(17,15,28,31,30,26,27,20,21,19)
> wilcox.test(smoker,nonsmokers, paired=FALSE)

   Wilcoxon rank sum test with continuity correction

data: smoker and nonsmokers
W = 24, p-value = 0.168
alternative hypothesis: true location shift is not equal to 0

Interpetation: Here pvalue is greater than 0.05 level of significance, we may fail to reject null hypothesis and conclude that smokers and non-smokers have same emotionality. so these data does not supported to Dr. Nesbitt’s data.

Assuming it follows assunptions of t-test,

> t.test(s,ns,var.equal=T)

   Two Sample t-test

data: s and ns
t = -1.4233, df = 16, p-value = 0.1739
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-9.397793 1.847793
sample estimates:
mean of x mean of y
19.625 23.400

Interpetation: Here pvalue is greater than 0.05 level of significance we may fail to reject null hypothesis and conclude that smokers and non-smokers have same emotionality. so these data does not supported to Dr. Nesbitt’s data.