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 32 62 77 69 240 50 or older 39 62 72 87 260

a) 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 What is your conclusion?

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)Applying chi square test :

Expected	Ei=row total*column total/grand total	fewer than 6	6 to 6.9	7 to 7.9	8 or more	Total
	49 or younger	34.080	59.520	71.520	74.880	240
	50 or older	36.920	64.480	77.480	81.120	260
	total	71	124	149	156	500
chi square    χ2	=(Oi-Ei)2/Ei	fewer than 6	6 to 6.9	7 to 7.9	8 or more	Total
	49 or younger	0.1269	0.1033	0.4199	0.4617	1.112
	50 or older	0.1172	0.0954	0.3876	0.4262	1.026
	total	0.244	0.199	0.807	0.888	2.1383

value of the X² test statistic =2.14

p value =0.5442

fail to reject Ho

b)

less then 6	14.2%
6 to 6.9 hours	24.8%
7 to 7.9 hours	29.8%
8 or more	31.2%