We have survey data on the body mass index (BMI) of 659 young women. The mean BM

Question

We have survey data on the body mass index (BMI) of 659 young women. The mean BMI in the sample was bar x =28. We treated these data as an SRS from a Normally distributed population with standard deviation sigma = 7. (a) Suppose that we had an SRS of just 125 young women. What would be the margin of error for 95% confidence? (Round your answer to four decimal places.) (b) Find the margins of error for 95% confidence based on SRSs of 406 young women and 1590 young women. (Round your answers to four decimal places.) (c) Compare the three margins of error. How does increasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same? Margin of error increases as n increases. Margin of error remains the same as n increases. Margin of error decreases as n increases. A laboratory scale is known to have a standard deviation of sigma = 0.001 gram in

Explanation / Answer

a) std error =std deviation/(n)1/2 =0.626

for 95% CI, z=1.96

hence margin of error =z*std error =1.2271

b) for n=406 ; margin of error =0.6809

for n=1590 ; margin of error =0.3441

c)margin of error decreases as n incvreases

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.