Over the years, projected due dates for expectant mothers have been notoriously bad at a large metropolitan hospital. The physicians attended an in-service program to develop techniques to improve their projections. In a recent survey of 100 randomly selected mothers who had delivered a baby at the hospital since the in-service, the average number of days to birth beyond the projected due date was 9.2 days with a standard deviation of 12.4 days.

a. Describe how to select the random sample of 100 mothers.

b. Estimate the mean number of days to birth beyond the due date using a 95% confidence interval. Interpret this interval.

c. If the mean number of days to birth beyond the due date was 13 days prior to the inservice, is there substantial evidence that the mean has been reduced? What is the level of significance of the test?

d. What factors may be important in explaining why the doctors' projected due dates are not closer to the actual delivery dates?