Question

Using the simple random sample of weights of women from a data​ set, we obtain these sample​ statistics: n equals = 35 and x =146.25 lb. Research from other sources suggests that the population of weights of women has a standard deviation given by sigma σ equals = 30.78 lb. a. Find the best point estimate of the mean weight of all women. b. Find a 95​% confidence interval estimate of the mean weight of all women.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 146.25

Population standard deviation =    = 30.78

Sample size = n =35

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 30.78 /  35 )

= 10.1974
At 95% confidence interval estimate of the population mean
is,

- E < < + E

146.25  - 10.1974 <   < 146.25  + 10.1974

136.0526<   < 156.4474

( 136.0526, 156.4474 )