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 40 61 77 62 240 50 or older 33 63 73 91 260 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). The p value is What is your conclusion? 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

Observed
	< 6	6 to 6.9	7 to 7.9	> 8	total
49 or younger	40	61	77	62	240
50 or older	33	63	73	91	260
Total	73	124	150	153	500

Ei = sum(rowi)*sum(coli)/total

Ex
	< 6	6 to 6.9	7 to 7.9	> 8
49 or younger	35.04	59.52	72	73.44
50 or older	37.96	64.48	78	79.56

a)

chi-square = sum((Oi - Ei)^2/Ei)

chi-square =5.5157

p-value = 0.1377

as p-value > 0.05, fail to reject H0.

b)

less than 6 hours = 73/500 = 0.134 = 14.6%

6 to 6.9 hours = 124/500 = 0.246 = 24.8%

7 to 7.9 hours = 150/500 = 30.0%

> 8 hours =153/500 = 30.6.%