The National Sleep Foundation used a survey to determine whether hours of sleepi

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 Age 49 or younger 50 or older 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 Fewer than 6 36 34 Hours of Sleep 6 to 6.9 63 60 7 to 7.9 80 79 8or more Total 240 260 61 87 Compute the value of the -test statistic (to 2 decimals) The p value is Select What is your conclusion? Select 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

Explanation / Answer

a) applyin chi square test of independece:

value of test statistic =3.91

p value =0.2713

as p value is greater than 0.05 ; conclusion : do not reject null

b)

dividing each category total with 500;

Observed Oi <6 6-6.9 7-7.9 >8 Total 49 or younger 36 63 80 61 240 50 or older 34 60 79 87 260 Total 70 123 159 148 500 Expected Ei=row*column/total <6 6-6.9 7-7.9 >8 Total 49 or younger 33.600 59.040 76.320 71.040 240 50 or older 36.400 63.960 82.680 76.960 260 Total 70 123 159 148 500 chi square =(Oi-Ei)2/Ei <6 6-6.9 7-7.9 >8 Total 49 or younger 0.1714 0.2656 0.1774 1.4189 2.033 50 or older 0.1582 0.2452 0.1638 1.3098 1.877 Total 0.330 0.511 0.341 2.729 3.91

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