Question

Do college students enjoy playing sports just as much as watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below. Playing Vs. Watching Sports Play 1 5 10 7 93 4 6 10 7 Watch 1 2 5 7 8 1 2 2 9 4 Assume a Normal distribution. What can be concluded at the the a=0.10 level of significance level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer v? Select an answer v (please enter a decimal) H: Select an answer ? v Select an answer (Please enter a decimal) b. The test statistic (please show your answer to 3 decimal places.) c. The p-value (Please show your answer to 4 decimal places.) d. The p-value is 2 v e. Based on this, we should Select an answer the null hypothesis. a

Answer 1

we should use repeated measure(matched paired study)

a)

null Hypothesis:μd		=	0
alternate Hypothesis: μd		≠	0

b)

S. No	Play	Watch	diff:(d)=x1-x2	d2
1	1	1	0	0.00
2	5	2	3	9.00
3	10	5	5	25.00
4	7	7	0	0.00
5	9	8	1	1.00
6	3	1	2	4.00
7	4	2	2	4.00
8	6	2	4	16.00
9	10	9	1	1.00
10	7	4	3	9.00
	total	=	Σd=21	Σd2=69
	mean dbar=	d̅     =	2.1000
	degree of freedom =n-1                            =		9
	Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		1.663330
	std error=Se=SD/√n=		0.5260
	test statistic            =	(d̅-μd)/Se         =	3.992

c)

p value

=

0.0031

from excel: tdist(3.992,9,2)

e)

reject the null

f)

The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude that the population mean rating for playing sports is not the same as the population mean rating for watching sports.