Question

0 Based on a random sample of 1140 adults, the mean amount of sleep per night is 8.42 hours. Assuming the population standard deviation for amount of sleep per night is 2.9 hours, construct and interpret a 95% confidence interval for the mean amount of sleep per night. A 95% confidence interval is (2.) (Round to two decimal places as needed.) Interpret the confidence interval. O A. We are 95% confident that the interval actually does contain the true value of the mean. OB. We are 95% confident that the interval actually does not contain the true value of the mean. OC. There is a 95% chance that the true value of the mean will not equal the mean of the interval. OD. There is a 95% chance that the true value of the mean will equal the mean of the interval Click to select your answer(s).

Answer 1

Solution :

Given that,

Sample size = n = 1140

Z$\alpha$/2 = 1.96

Margin of error = E = Z$\alpha$/2* ($\sigma$ /$\sqrt$n)

= 1.96 * (2.9 / $\sqrt$ 1140)

Margin of error = E = 0.17

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

$\bar x$ - E < $\mu$ < $\bar x$ + E

8.42 - 0.17 < $\mu$ < 8.42 + 0.17

8.25 < $\mu$ < 8.59

A 95% confidence interval is (8.25 , 8.59)

option A. is correct