(16.09) We have the survey data on the body mass index (BMI) of 646 young women.
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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 1635Explanation / 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.
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