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 63 78 69 240 50 or older 40 64 72 84 260

Answer 1

here null hypothesis:Ho:  hours of sleeping per night are independent of age

alternate hypothesis:Ha: hours of sleeping per night are not independent of age

degre of freedom =(row-1)*(column-1)=(2-1)*(4-1)=3

for 3 df and 0.05 level rejection region >7.815

Observed	OBS	<6	6-6.9	7-7.9	>8	Total
	49 or yunger	30	63	78	69	240
	50 or older	40	64	72	84	260
	Total	70	127	150	153	500
Expected	Ei=?row*?column/?total	<6	6-6.9	7-7.9	>8	Total
	49 or yunger	33.600	60.960	72.000	73.440	240
	50 or older	36.400	66.040	78.000	79.560	260
	Total	70	127	150	153	500
chi square	=(Oi-Ei)2/Ei	<6	6-6.9	7-7.9	>8	Total
	49 or yunger	0.39	0.07	0.50	0.27	1.22
	50 or older	0.36	0.063	0.462	0.248	1.13
	Total	0.74	0.13	0.96	0.52	2.351

here as test statistic 2.351 is not i n critical region we can not reject null hypotesis

we do not have sufficient evidence at 0.05 level to conclude that  hours of sleeping per night are not independent of age