Question

Exercise 5 (15) In the process of learning how to conduct a sign test, each student inevitably punches their computer screen several times. I have found that students who punch their screens during this exercise can be separated into two categories. The first category believes that this statistics course would be better if they did all of their statistics by hand. The second category is pleased that the course is taught using R. Below is the number of times a computer screen is punched by a student in each category. Assume all assumptions have been met.

Hates R	Loves R
3	7
6	10
7	11
4	8
5	9

1. By hand, test the hypothesis that there is no difference between the two categories in relation to how many times they punch their computer screen. Provide the scrap paper used to conduct this test.

2. By hand, calculate the 95% CI of the difference between the means.

Answer 1

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

Hates R	Loves R
3	7
6	10
7	11
4	8
5	9
	Hates R	Loves R
	5.00	9.00	mean
	1.58	1.58	std. dev.
	5	5	n
		8	df
		-4.000	difference (Hates R - Loves R)
		2.500	pooled variance
		1.581	pooled std. dev.
		1.000	standard error of difference
		0	hypothesized difference
		-4.000	t
		.0039	p-value (two-tailed)
		-6.306	confidence interval 95.% lower
		-1.694	confidence interval 95.% upper
		2.306	margin of error

The p-value is 0.0039.

Since the p-value (0.0039) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we cannot conclude that there is no difference between the two categories in relation to how many times they punch their computer screen.

The 95% CI of the difference between the means is between -6.306 and -1.694.

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