(use R software to answer this question step by step) Students in an introductor
ID: 3301525 • Letter: #
Question
(use R software to answer this question step by step)
Students in an introductory statistics class were asked at the beginning of the course and at the end of the course the extent to which they disagreed or agreed with the following statement: “Statistics is important to my major area of study.” They responded on a scale of 1 to 5, with (1) strongly disagree, (2) moderately disagree, (3) neutral, (4) moderately agree, and (5) strongly agree. The data are:
before, after
2,2
3,4
4,4
4,4
3,4
1,4
3,3
4,5
4,4
5,4
3,4
4,5
2,4
2,2
4,5
3,5
4,4
2,1
2,2
a) Explain why the Wilcoxon signed-ranks test may be more appropriate than the paired t-test for these data.
b) Did students’ opinion of the importance of statistics increase? Support your answer.
Explanation / Answer
Answer:
R code:
before<-c(2,3,4,4,3,1,3,4,4,5,3,4,2,2,4,3,4,2,2)
after<-c(2,4,4,4,4,4,3,5,4,4,4,5,4,2,5,5,4,1,2)
shapiro.test(before); shapiro.test(after)
wilcox.test(before,after, alternative = "less", paired=TRUE)
a). Explain why the Wilcoxon signed-ranks test may be more appropriate than the paired t-test for these data.
R output for normality test:
Shapiro-Wilk normality test
data:before
W = 0.90422, p-value = 0.05803
Shapiro-Wilk normality test
data:after
W = 0.81839, p-value = 0.002141
Since after data is significant at 0.05 level, after data not follows normal, paired t test is not appropriate.
b) Did students’ opinion of the importance of statistics increase? Support your answer.
Wilcoxon signed rank test with continuity correction
data: before and after
V = 9, p-value = 0.01451
alternative hypothesis: true location shift is less than 0
calculated P=0.01451 which is < 0.05 level of significance, null hypothesis is rejected.
There is sufficient evidence to conclude that students’ opinion of the importance of statistics increase.
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