A study was done on pregnant women who smoke during their pregnancies. In particular, the researchers wanted to study the effect that smoking has on the pregnancy length. A sample 114 pregnant women who were smokers participated in the study and were followed until the birth of their child. At the end of the study, the collected data were analyzed and it was found that the average pregnancy length of the 114 women was 260 days. From a large body of research, it is known that the length of human pregnancy has a standard deviation of 16 days.

In the previous activity, we calculated a 95% confidence interval for μ, the mean pregnancy length of women who smoke during their pregnancy based on the given information, and found it to be 260 +/- 3, or (257, 263).

Assume now that the researcher wants to get a more precise interval estimation by reducing the margin of error from 3 to 2 while maintaining the same level of confidence. How many additional smoking pregnant women should the researcher sample? (Hint: calculate first what the total sample size must be in order to achieve this).