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.%

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 32 62 77 69 240 50 or older 39...

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
65
70
65
240
50 or older
31...

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
Hours of sleep- fewer than 6
6 to 6.9
7 to 7.9
8 or more
Total
49 or younger
34
62
72
72
240
50 or older
37...

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
39
55
70
76
240
50 or older
30...

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
37
61
74
68
240
50 or older
33...

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
33
59
72
76
240
50 or older
33...

A survey was conducted to determine whether hours of sleep per
night are independent of age. A sample of individuals was asked to
indicate the number of hours of sleep per night with categorical
options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8
hours or more. Later in the survey, the individuals were asked to
indicate their age with categorical options: age 39 or younger and
age 40 or older. Sample data follow.
Hours...

A survey was conducted to determine whether hours of sleep per
night are independent of age. A sample of individuals was asked to
indicate the number of hours of sleep per night with categorical
options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8
hours or more. Later in the survey, the individuals were asked to
indicate their age with categorical options: age 39 or younger and
age 40 or older. Sample data follow.
Hours...

A survey was conducted to determine whether hours of sleep per
night are independent of age. A sample of individuals was asked to
indicate the number of hours of sleep per night with categorical
options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8
hours or more. Later in the survey, the individuals were asked to
indicate their age with categorical options: age 39 or younger and
age 40 or older. Sample data follow.
Hours...

You may need to use the appropriate technology to answer this
question.
A survey was conducted to determine whether hours of sleep per
night are independent of age. A sample of individuals was asked to
indicate the number of hours of sleep per night with categorical
options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8
hours or more. Later in the survey, the individuals were asked to
indicate their age with categorical options: age...

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