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	30	64	76	70	240
	50 or older	30	58	80	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 X2 (Chi2) test statistic (to 2 decimals).????

b) 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)

Following table shows the row total and column total:

Hours of Sleep
	Age	Fewer than 6	6 to 6.9	7 to 7.9	8 or more	Total
	49 or younger	30	64	76	70	240
	50 or older	30	58	80	92	260
	Total	60	122	156	162	500

Expected frequencies will be calculated as follows:

Following table shows the expected frequency:

Hours of Sleep
Age	Fewer than 6	6 to 6.9	7 to 7.9	8 or more	Total
49 or younger	28.8	58.56	74.88	77.76	240
50 or older	31.2	63.44	81.12	84.24	260
Total	60	122	156	162	500

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
30	28.8	0.05
64	58.56	0.505355191
76	74.88	0.016752137
70	77.76	0.774403292
30	31.2	0.046153846
58	63.44	0.466481715
80	81.12	0.015463511
92	84.24	0.714833808
Total		2.5894435

The test statistics is:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(4-1)=4

The p-value is: 0.4593

Since p-value is greater than 0.05 so we fail to reject the nul hypothesis.

b)

Following table shows the required percentage:

	Frequency, f	(f*100)/500%
Fewer than 6	60	12
6 to 6.9	122	24.4
7 to 7.9	156	31.2
8 or more	162	32.4