Question

he National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older.

Hours of Sleep
	Age	Fewer than 6	6 to 6.9	7 to 7.9	8 or more	Total
	49 or younger	39	57	76	68	240
	50 or older	34	55	77	94	260

1. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use  = .05. Use Table 12.4.
   
   Compute the value of the  ² test statistic (to 2 decimals).
   
   
   The p value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2
   
   What is your conclusion?
   SelectConclude age and hours of sleep are not independentCannot reject the assumption that age and hours of sleep are independentItem 3
   
2. Using the total sample of 500, estimate the percentage of people who sleep less than 6, 6 to 6.9, 7 to 7.9, and 8 or more hours on weeknights (to 1 decimal).
   

   Less than 6 hours	%
   6 to 6.9 hours	%
   7 to 7.9 hours	%
   8 or more hours	%

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	<6	6-6.9	7-7.9	>8	Total
	49 or younger	35.040	53.760	73.440	77.760	240.00
	50 or older	37.960	58.240	79.560	84.240	260.00
	total	73.00	112.00	153.00	162.00	500.00
chi square    χ2	=(Oi-Ei)2/Ei	<6	6-6.9	7-7.9	>8	Total
	49 or younger	0.448	0.195	0.089	1.225	1.9571
	50 or older	0.413	0.1802	0.0824	1.1308	1.8065
	total	0.8606	0.3755	0.1716	2.3558	3.764
test statistic X2 =		3.76

p value =

0.2882

or p value >0.10

Cannot reject the assumption that age and hours of sleep are independent

b)

<6	14.6%
6-6.9	22.4%
7-7.9	30.6%
>8	32.4%