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a. The point estimate of the married people that sleep well is = 0.6299. The confidence interval for the mean hours of sleep for those that have never been married but report good sleep is 0.6186, 0.6412
b. The point estimate of the number of hours for people that have never been married = 7.2257
95% confidence interval for the mean number of hours of sleep for those who have never been married = 7.2065, 7.2447
c. the estimated number of sleep for those that have never been married = 7.729 hours
a. The point estimate
Those who have never been married n = 7044
Xp = those who sleep for 7 hours at least
To get Xp, the <u>excel function </u>
Countif(range, criteria)
Countif(A:A, >=7)
This gives Xp = 4437
Point estimate =
= 0.6299
The point estimate of the married people that sleep well is = 0.6299
At 95% interval of confidence,
α = 1-0.95 = 0.05
α/2 = 0.05/2 = 0.025
Z0.025 = 1.96 ( Use the standard probability normal table)
Margin of Error
=
= 0.0113
The 95% confidence interval
= 0.6299 - 0.0113 , 0.6299 + 0.0113
= 0.6186, 0.6412
The confidence interval for the mean hours of sleep for those that have never been married is 0.6186, 0.6412
b. Sample mean
x = ∑x/n
x = number of sleep of the never been married
Mean is calculated using excel function
Average(range)
Average(a:a)
This gives the sample mean = 7.2257
The point estimate of the number of hours for people that have never been married = 7.2257
<u>Standard deviation</u> using excel =
Stdev(A:A) = 0.8211
= 0.0192
The<u> confidence interval</u> =
= 7.2257-0.0192, 7.2257+0.0192
= 7.2065, 7.2447
95% confidence interval for the mean number of hours of sleep for those who have never been married = 7.2065, 7.2447
c. From the available data, the mean number of sleep per day that is gotten from the 4437 people that are unmarried and sleep healthily for at least 7 hours = 34295.1
Mean = 34295.1/4437
= 7.729
the estimated number of sleep for those that have never been married = 7.729 hours
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