Question

Returning to the same study examining the relationship between maternal smoking during pregnancy and congenital malformations (among children who suffer from an abnormality other than Down's Syndrome or an oral cleft, 32.8% have mothers who smoked during pregnancy), consider children born with an oral cleft. In a random sample of 27 such infants, 15 have mothers who smoked during pregnancy.

a) What is a point estimate for p? Construct a 95% confidence interval for the population proportion.

b) Conduct the test at the 0.01 level of significance. (I am looking for the p-value)

Answer 1

(a) A point estimate for p=15/27=0.56

Given a=0.05, |Z(0.025)|=1.96 (from standard normal table)

So 95% confidence interval is

p+/- Z*v(p*(1-p)/n)

--> 0.56 +/- 1.96*sqrt(0.56*(1-0.56)/27)

--> (0.3727618, 0.7472382)

(b) The test hypothesis is

Ho:p=0.328

Ha:p not equal to 0.328

The test statistic is

Z=(phat-p)/v(p*(1-p)/n)

=(0.56-0.328)/sqrt(0.328*(1-0.328)/27)

=2.57

The p-value=2*P(Z>2.57)=0.0102 (from standard normal table)

Since p-value is larger than 0.005, we do not reject HO.