Question

The 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	33	59	72	76	240
	50 or older	33	57	77	93	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

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	<6	6-6.9	7-7.9	8 or more	Total
	49 or young	31.6800	55.6800	71.5200	81.1200	240.00
	50 or older	34.3200	60.3200	77.4800	87.8800	260.00
	total	66.00	116.00	149.00	169.00	500.00
chi square    χ2	=(Oi-Ei)2/Ei	<6	6-6.9	7-7.9	8 or more	Total
	49 or young	0.0550	0.198	0.003	0.323	0.5793
	50 or older	0.051	0.1827	0.0030	0.2983	0.5348
	total	0.1058	0.3807	0.0062	0.6215	1.114
test statistic X2 =		1.11

p value is greater than 0.10

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

b)

<6	13.2%
6-6.9	23.2%
7-7.9	29.8%
8 or more	33.8%