Question

A study of women’s weights found that a randomly selected sample of 150 women had a mean weight of 147.3 lb. Assuming that the population standard deviation is 19.6 lb., construct a 95% confidence interval estimate of the mean weight of all women. Choose the correct interval from below:

Choose one • 10 points

• (144.211, 150.389)

• (140.611, 146.789)

• (144.667, 149.933)

• (144.163, 150.437)

Answer 1

Solution:

Confidence interval for Population mean

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

We are given

Xbar = 147.3

σ = 19.6

n = 150

Confidence level = 95%

Z = 1.96

(by using z-table)

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

Confidence interval = 147.3 ± 1.96*19.6/sqrt(150)

Confidence interval = 147.3 ± 1.96*1.6003

Confidence interval = 147.3 ± 3.1366

Lower limit = 147.3 - 3.1366 = 144.163

Upper limit = 147.3 + 3.1366 = 150.437

Confidence Interval = (144.163, 150.437)

Last alternative is correct.