Question

The U.S. Department of Health, Education, and Welfare collected sample data for 1555 women aged 18 to 24 years.  This sample group has a mean  μ serum cholesterol level (measured in mg/100 ml) of 193.7. Use this sample data to find the 97% confidence interval for the mean serum cholesterol level of all women in the 18- 24 year age bracket. Assume that the population standard deviation  σ is 42.0.

Group of answer choices

(189.21 , 193.83 )

(191.39 , 196.01)

none of these

( 189.42 , 193.98 )

Answer 1

We have to find 97% confidence interval for mean serum cholesterol level of all women in 18-24 year age bracket

xbar - E < < xbar + E

Where E = Z​​​​​​a/2* ( /√n)

For a = 0.03 , Z​​​​​​a/2 = Z​​​​​​0.015 = 2.17

E = 2.17 *(42/√1555)

E = 2.31

193.7 - 2.31 <   < 193.7 + 2.31

191.39 <   < 196.01

So 97% confidence interval for mean serum cholesterol level of all women in 18-24 age bracket is ( 191.39 , 196.01)