Question

In: Statistics and Probability

Based on a random sample of 1040 adults, the mean amount of sleep per night is...

Based on a random sample of 1040 adults, the mean amount of sleep per night is 8.26 hours. Assuming the population standard deviation for the amount of sleep per night is 2.7 hours, construct and interpret a 95% confidence interval for the mean amount of sleep per night.

A 95% confidence interval is (, ) Interpret the confidence interval.

Interpret the confidence Interval:

A. We are 95% confident that the interval actually does contain the true value of the mean.

B. There is a 95% chance that the true value of the mean will not equal the mean of the interval.

C. There is a 95% chance that the true value of the mean will equal the mean of the interval.

D. We are 95% confident that interval actually does not contain the true value of the man.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 8.26

Population standard deviation = = 2.7

Sample size = n = 1040

Z_/2 = 1.96

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 1.96 * (2.7 / $\sqrt$ 1040)

= 0.16

At 95% confidence interval estimate of the population mean is,

- E < < + E

8.26 - 0.16 < < 8.26 +0 16

8.10 < < 8.42

(8.10 , 8.42)

A. We are 95% confident that the interval actually does contain the true value of the mean.

orchestra answered 2 years ago

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