The CDC recently reported that among women in the United States with a pregnancy

Question

The CDC recently reported that among women in the United States with a pregnancy complicated by gestational diabetes mellitus (GDM), 20% delivered a baby that was large for gestational age (LGA). Suppose you design a nationwide study in which you collect data on a sample of 500 women with GDM, and find that 75 had an LGA infant. a. Compute a 95% CI for the proportion of women with an LGA Infant, based on your sample data. Remember to first check any necessary assumptions. b. State whether the proportion of women who had an LGA infant is significantly different than the CDC-reported proportion of 20%, at a 5% significance level, and justify your answer. c. Suppose you wanted to estimate a 95% CI for the proportion of GDM women with an LGA infant, but with only a 1% margin of error. What is the total number of women with GDM you would need to enroll in your study?

Explanation / Answer

a)

here estimated proportion phat =75/500=0.15

for n=500 ; as np >10 and n(1-p) >10 therefore normal model can be applied

std error =(phat(1-phat)/n)1/2 =0.016

for 95% CI ; z=1.96

therefore 95% confidence interval =phat -/+ z*std errror =0.1187 ; 0.1813

b) as above interval does not contain 20% as possible value we have significant evidence of difference then the CDC reported proportion of 20%.

c)

here margin of error E =0.01

for 95% CI ; z=1.96

here estimated proportion p=0.15

therefore sample size requried n=p(1-p)*(Z/E)2 =4898

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