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.

a. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use ? = .05.

Compute the value of the test statistic (to 2 decimals)

Answer:

The p value is

Answer (to four decimal places):

Can you reject the assumption that age and hours of sleep are independent?

Answer: (yes or no)

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

Answer % :

6 to 6.9 hours Answer % :

7 to 7.9 hours Answer % :

8 or more hours Answer % :

Hours of Sleep Age Fewer than 6   6 to 6.9    7 to 7.9 8 or more   Total 49 or younger 33 61 71 75 240 50 or older 32 61 70 97 260

Explanation / Answer

applying chi square test:

value of the test statistic=2.040

p value is =0.5642

as p value is very high

no

b)

Observed Oi <6 6-6.9 7-7.9 >8 Total Yes 33 61 71 75 240 No 32 61 70 97 260 Total 65 122 141 172 500 Expected Ei=?row*?column/?total <6 6-6.9 7-7.9 >8 Total Yes 31.2000 58.5600 67.6800 82.5600 240 No 33.8000 63.4400 73.3200 89.4400 260 Total 65 122 141 172 500 chi square =(Oi-Ei)2/Ei <6 6-6.9 7-7.9 >8 Total Yes 0.1038 0.1017 0.1629 0.6923 1.061 No 0.0959 0.0938 0.1503 0.6390 0.979 Total 0.200 0.196 0.313 1.331 2.040

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