A random sample of birth weights of 186 babies has a mean of 3,103 g and a stand

Question

A random sample of birth weights of 186 babies has a mean of 3,103 g and a standard deviation of 696 g (based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure,” by Singer et al., Journal of the American Medical Association, Vol. 291, No. 20). Those babies were born to mothers who did not use cocaine during their pregnancies.

What is the best point estimate of the mean weight of babies born to mothers who did not use cocaine during their pregnancies?
Construct a 95% confidence interval estimate of the mean birth weight for all such babies.
Compare the confidence interval from part (b) to this confidence interval obtained from birth weights of babies born to mothers who used cocaine during pregnancy: 2,608 g < µ < 2,792 g. Does cocaine use appear to affect the birth weight of a baby?

Explanation / Answer

best point estimate of the mean weight of babies born to mothers who did not use cocaine during their pregnancies

=3103 g

here std error of mean =std deviation/(n)1/2 =51.033

for 95% CI, z=1.96

hence confidence interval =sample mean -/+z*std error =3003 <µ<3203

Yes cocaine use appear to affect the birth weight of a baby , as our confidence interval lowest value is above then highest value of confidence interval obtained from birth weights of babies born to mothers who used cocaine during pregnancy.

Therefore we can conclude that cocaine use appear to affect the birth weight of a baby

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