Question

The Centers for Disease Control and Prevention (CDC) defines a healthy sleep duration

Answer 1

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

$P=\frac{Xp}{n}$

$Xp = successes\\n = sample size$

Those who have never been married n = 7044

Xp = those who sleep for 7 hours at least

To get Xp, the excel function

Countif(range, criteria)

Countif(A:A, >=7)

This gives Xp = 4437

Point estimate =

$\frac{4477}{7044}$

= 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

=$M.E = 1.96\sqrt \frac{0.6299(1-0.6299)}{7044} \\\\= 1.96\sqrt{0.000033} \\\\1.96*0.0057$

= 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

Standard deviation using excel =

Stdev(A:A) = 0.8211

$Margin of error =1.96*\frac{0.8211}{\sqrt{7044} }$

= 0.0192

The confidence interval =

= 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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