Question

According to a government​ agency, the average workweek for an adult in February February 2018 was 32.3 hours. Assume the population standard deviation for the number of hours worked per week is 6.0 hours. A random sample of 35 adults worked an average of 33.3 hours last week.

b. Identify the symmetrical interval that includes 96​% of the sample means if the true population mean is 32.3 hours per week. (lower bound and upper bound)

Answer 1

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

We are given

Xbar = 33.3

σ = 6.0

n = 35

Confidence level = 96%

Critical Z value = 2.0537

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 33.3 ± 2.0537*6/sqrt(35)

Confidence interval = 33.3 ± 2.0537*1.0142

Confidence interval = 33.3 ± 2.0829

Lower limit = 33.3 - 2.0829 = 31.22

Upper limit = 33.3 + 2.0829 = 35.38

Confidence interval = (31.22, 35.38)