One of the variables collected in the North Carolina Birth Registry is pounds gained during pregnancy. According to data from the entire registry in 2001, the number of pounds gained during pregnancy was approximately normally distributed with a mean of 30.23 pounds and a standard deviation of 13.84 pounds. Suppose we now considered these to be estimates from a sample of n observations. What would be our 95% confidence interval around this estimate of the mean if:
a. The sample size n = 5?
b. The sample size n = 25?
c. The sample size n = 121?
d. What do these results tell you in practical terms about the relative benefits of increasing the sample size from 5 to 25? From 25 to 121?