There are two parts to the qustion thanks Based on a random sample of 1180 adult
ID: 3240720 • Letter: T
Question
There are two parts to the qustion thanks
Based on a random sample of 1180 adults, the mean amount of sleep per night is 7.55 hours. Assuming the population standard deviation for amount of sleep per night is 1.4 hours, construct and interpret a 95% confidence interval for the mean amount of sleep per night.
A 95% confidence interval is ( __,__ ). (Round to two decimal places as needed.)
Interpret the confidence interval.
A.We are 95% confident that the interval actually does not 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 the interval actually does contain the true value of the mean.
Explanation / Answer
Solution:
Given n = 1180
mean x = 7.55
Standard deviation = 1.4
= 1-0.95 = 0.05
Z/2 = Z(0.05/2) = Z(0.025) = 1.96
Standard error SE = /n
= 1.4/1180
= 0.0408
Confidence interval = x ± Z/2 * SE
= 7.55 ± 1.96 * 0.0408
= (7.47, 7.63)
A.We are 95% confident that the interval actually does not contain the true value of the mean.
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