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(16.09) We have the survey data on the body mass index (BMI) of 646 young women.

ID: 3151900 • Letter: #

Question

(16.09) We have the survey data on the body mass index (BMI) of 646 young women. The mean BMI in the sample was x=26.6. We treated these data as an SRS from a Normally distributed population with standard deviation =7.4.

Find the margins of error for 90% confidence based on SRSs of N young women.

(16.09) We have the survey data on the body mass index (BMI) of 646 young women. The mean BMI in the sample was x=26.6. We treated these data as an SRS from a Normally distributed population with standard deviation =7.4.

Find the margins of error for 90% confidence based on SRSs of N young women.

N margins of error (±0.0001) 110 370 1635

Explanation / Answer

The formula to be used to find margin of error :

E = Zc * / n

Where Zc = critical value of Z for given confidence level

= population standard deviation

n = sample size

Zc for 90% confidence level = 1.645

= 7.4

For N = 110

E = 1.645 * 7.4 / 110

E = 12.173/10.4881

E = 1.1606 [margin of error is + & - both]

For N = 370

E = 1.645 * 7.4 / 370

E = 12.173/ 19.2354

E = 0.6328 [margin of error is + & - both]

For N = 1635

E = 1.645 * 7.4 / 1635

E = 12.173/ 40.4351

E = 0.3011 [margin of error is + & - both]

We observe that as sample size increases, the margin of error decreases.