Question

InatestoftheAtkinsweightlossprogram,30randomlyselectedoverweight individuals participated in a randomized trial. After one year, the mean weight loss was found to be 3 lbs, with a standard deviation of 5.36 lbs. Find a 95% confidence interval for the mean weight loss of all overweight adults who follow the Atkins program?

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 3

Population standard deviation =    =5.36

Sample size n =30

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* ( 5.36/ 30 )

= 1.9
At 95% confidence interval mean
is,

- E < < + E

3 - 1.9 <   < 3 + 1.9

(1.1 , 4.9)