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	36	55	79	70	240
	50 or older	33	63	72	92	260

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).
  

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:

Observed	Oi	<6	6-6.9	7-7.9	>8	Total
	<49	36	55	79	70	240
	>50	33	63	72	92	260
	Total	69	118	151	162	500
Expected	Ei=Σrow*Σcolumn/Σtotal	<6	6-6.9	7-7.9	>8	Total
	<49	33.120	56.640	72.480	77.760	240
	>50	35.880	61.360	78.520	84.240	260
	Total	69	118	151	162	500
chi square    χ2	=(Oi-Ei)2/Ei	<6	6-6.9	7-7.9	>8	Total
	<49	0.250	0.048	0.587	0.774	1.659
	>50	0.231	0.044	0.541	0.715	1.531
	Total	0.482	0.091	1.128	1.489	3.190

chi square test statsitic =3.19

as test statistic is less then crtiical value 7.815 ; we fail to reject null hypothesis

less then 6	13.80%
6 to 6.9 hours	24%
7 to 7.9 hours	30.2%
8 or more	32.4%