It seems when people are under stress they are more likely t

It seems when people are under stress they are more likely to make errors in pronunciation. A group of students hypothesized that discussing a stressful topic would decrease the likelihood of someone clearly enunciating their words. To test this hypothesis, they first recorded students talking about a non-stressful topic, and then they recorded the same students talking about a stressful topic. They identified the number of words that were not fully enunciated for the first 100 words each subject uttered in each condition. The results from the 11 participants are presented here:

Student

Non-stressful

Stressful

1

1

2

2

2

2

3

0

3

4

5

6

5

3

2

6

2

3

7

1

3

8

4

5

9

6

7

10

7

7

11

2

4

A. What test is appropriate for testing whether stress may influence enunciation using these data?

B. State the null and alternative hypothesis both in words and in equations.

C. Conduct a two-tailed test at a ?=0.05 significance level:

Ca) By hand using a calculator

Cb) Using the statistical software JMP

D. Write a brief conclusion based on your findings.

Student	Non-stressful	Stressful
1	1	2
2	2	2
3	0	3
4	5	6
5	3	2
6	2	3
7	1	3
8	4	5
9	6	7
10	7	7
11	2	4

Solution

The null hypothesis is: here is no significant difference between the two population means.

The alternative hypothesis is: there is a significant difference between the two population means.

The degrees of freedom is df=11+11-2=20

The pooled variance is: ((11-1)*2.236^2+(11-1)*1.949^2)/20=4.39

The estimated standard error is root over(4.39/11+4.39/11)=0.88

The test statistic is:((3-4)-0)/0.88=-1.13

The critical value is: -2.086

Since, the test statistic does not fall in the critical thus fail to reject the null hypothesis. So, the test is not significant at 0.05 level of significance.