Question

You may need to use the appropriate technology to answer this question.

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.

Hours of Sleep	Age Group
	39 or younger	40 or older
Fewer than 6	36	34
6 to 6.9	62	59
7 to 7.9	77	75
8 or more	65	92

Find the value of the test statistic. (Round your answer to three decimal places.)

_____________

What is the p-value? (Round your answer to four decimal places.)

p-value =_______________

What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

Fewer than 6_______ %

6 to 6.9_________ %

7 to 7.9________ %

8 or more______ %

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	<39	>40	Total
	<6	33.6000	36.4000	70
	6-6.9	58.0800	62.9200	121
	7-7.9	72.9600	79.0400	152
	>8	75.3600	81.6400	157
	total	240	260	500
chi square    χ2	=(Oi-Ei)2/Ei	<39	>40	Total
	<6	0.171	0.158	0.3297
	6-6.9	0.265	0.244	0.5088
	7-7.9	0.224	0.206	0.4302
	>8	1.424	1.315	2.7389
	total	2.0839	1.9236	4.0076
test statistic X2 =		4.008
p value =		0.2606

2)

less than 6 hours=(70/500)*100=		14.0%
6 to 6.9 hours=(121/500)*100=		24.2%
7 to 7.9 hours=(152/500)*100=		30.4%
8 or more hours=(157/500)*100		31.4%