In the paper “Persistent Pulmonary Hypertension of the Neonate and Asymmetric Growth Restriction” M. Williams et al. reported on a study of characteristics of neonates. Infants treated for pulmonary hypertension, called the PH group, were compared with those not so treated, called the control group. One of the characteristics measured was head circumference. The mean head circumference of the 10 infants in the PH group was 34.2 centimeters (cm).

a. Assuming that head circumferences for infants treated for pulmonary hypertension are normally distributed with standard deviation 2.1 cm, determine a 90% confidence interval for the mean head circumference of all such infants.

b. Obtain the margin of error, E, for the confidence interval you found in part (a).

c. Explain the meaning of E in this context in terms of the accuracy of the estimate.

d. Determine the sample size required to have a margin of error of 0.5 cm with a 95% confidence level.