Question

A study of women’s weights found that a randomly selected sample of 234 women had a mean weight of 157.3 lb. Assuming that the population standard deviation is 15.6 lb., construct a 95% confidence interval estimate of the mean weight of all women.

Answer 1

(155.301 ; 159.299)

Explanation:

Xbar = 157.3

Sample size, n = 234

Population standard deviation, σ = 15.6

The confidence interval :

Xbar ± standard Error

Standard Error = Zcritical * σ/√n

Zcritical at 95% = 1.96

Standard Error = 1.96 * (15.6/√234) = 1.999

Lower boundary : 157.3 - 1.999 = 155.301

Upper boundary : 157.3 + 1.999 = 159.299

(155.301 ; 159.299)