Question

A study was conducted to investigate the relationship between maternal smoking during pregnancy and the presence of congenital malformations in the child. Among children who suffer from an abnormality other than Down’s syndrome or an oral cleft, 32.8% have mothers who smoked during pregnancy. You wish to determine if this proportion is the same for those children born with an oral cleft. In a random sample of 27 infants with an oral cleft, 15 had mothers who smoked during pregnancy.

a. What is the estimate of the proportion of infants born with oral clefts whose mothers smoked during pregnancy?

b. Construct a 95% confidence interval for the true population proportion.

c. What are the Null and Alternative Hypotheses of this test?

d. Conduct the test at the 0.05 level of significance.

e. Using Stata, determine the sample size required to have 80% power to detect an alternative of 40% at the 0.01 level of significance.

Answer 1

A study was conducted to investigate the relationship between maternal smoking during pregnancy and the presence of congenital malformations in the child. Among children who suffer from an abnormality other than Down’s syndrome or an oral cleft, 32.8% have mothers who smoked during pregnancy. You wish to determine if this proportion is the same for those children born with an oral cleft. In a random sample of 27 infants with an oral cleft, 15 had mothers who smoked during pregnancy.

a. What is the estimate of the proportion of infants born with oral clefts whose mothers smoked during pregnancy?

p =15/27 =0.5556

b. Construct a 95% confidence interval for the true population proportion.

Confidence Interval Estimate for the Proportion
Data
Sample Size	27
Number of Successes	15
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.5556
Z Value	1.9600
Standard Error of the Proportion	0.0956
Interval Half Width	0.1874
Confidence Interval
Interval Lower Limit	0.3681
Interval Upper Limit	0.7430

95% CI = (0.3681, 0.7430)

c. What are the Null and Alternative Hypotheses of this test?

d. Conduct the test at the 0.05 level of significance.

=2.5185

Rejection Region: Reject Ho if z < -1.96 or z > 1.96

Calculated z = 2.5185 , in the rejection region

The null hypothesis is rejected.

This proportion (0.328) is not the same for those children born with an oral cleft.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.328
Level of Significance	0.05
Number of Items of Interest	15
Sample Size	27
Intermediate Calculations
Sample Proportion	0.5556
Standard Error	0.0904
Z Test Statistic	2.5185
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0118
Reject the null hypothesis

e. Using Stata, determine the sample size required to have 80% power to detect an alternative of 40% at the 0.01 level of significance.

power oneproportion 0.5556 0.4, test(wald) alpha(0.01)

Performing iteration ...

Estimated sample size for a one-sample proportion test

Wald z test

Ho: p = p0 versus Ha: p != p0

Study parameters:

        alpha =    0.0100

        power =    0.8000

        delta =   -0.1556

           p0 =    0.5556

           pa =    0.4000

Estimated sample size:

            N =       116