Question

A researcher wants to determine how many hours of sleep adults get per night. She asks a random sample of 32 adults how many hours of sleep they get per night. The mean of their answers is 7.1 hours, and the standard deviation is 1.5 hours. Make a 95% confidence interval for the mean number of hours of sleep per night for adults. Round the end points of the confidence interval to 2 decimal points.

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 7.1

S = 1.5

n = 32

df = n – 1 = 31

Confidence level = 95%

Critical t value = 2.0395

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 7.1 ± 2.0395*1.5/sqrt(32)

Confidence interval = 7.1 ± 0.5408

Lower limit = 7.1 - 0.5408 = 6.56

Upper limit = 7.1 + 0.5408 = 7.64

Confidence interval = (6.56, 7.64)