The National Sleep Foundation used a survey to determine whether hours of sleepi
ID: 3204373 • Letter: T
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 Fewer than 6 6 to 6.9 7 to 7.9 8 or more Total
49 or younger 32 65 73 70 240
50 or older 36 55 77 92 260
Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use = .05.
1.) Compute the value of the 2 test statistic (to 2 decimals). ______
2.) The p value is?_______
3.) 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 ______%
Explanation / Answer
here of test of independence we use chi square test:
here degree of freedom =(row-1)*(column-1) =(4-1)*(2-1) =3
here test statistic X2 =3.368
for which p value at 3 degree of freedom =0.3382
as p value is greater then 0.05 level, we cna not reject the null hypothesis that thses are independent,
3) from above estimation of less then 6 hours =(68/500) *100 =13.6%
6 to 6.9 hours =(120/500) *100 =24%
7-7.9 hours =(150/500)*100 =30%
>8 hours =(162/500)*100 =32.4%
Observed O <6 6-6.9 7.-7.9 >8 Total 49 or younger 32 65 73 70 240 50 or older 36 55 77 92 260 Total 68 120 150 162 500 Expected E=rowtotal*column total/grand total <6 6-6.9 7.-7.9 >8 Total 49 or younger 32.640 57.600 72.000 77.760 240 50 or older 35.360 62.400 78.000 84.240 260 Total 68 120 150 162 500 chi square =(O-E)^2/E <6 6-6.9 7.-7.9 >8 Total 49 or younger 0.013 0.951 0.014 0.774 1.752 50 or older 0.012 0.878 0.013 0.715 1.617 Total 0.024 1.828 0.027 1.489 3.368