Question

in a study of the impact of smoking on birth weight, researchers analyze birth weights (in grams) for babies born to 189 women who gave birth in 1989 at a hospital in massachusetts. in the group, 74 of the women were categorized as \smokers\ and 115 as
onsmokers.\ the difference in the two - sample mean birth weights (nonsmokers minus smokers) is 281.7 grams and the 95% confidence interval is (76.5, 486.9). which gives the best interpretation of what we can conclude about the impact of smoking on birth weight? a. when smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies of nonsmokers is between 76.5 grams to 486.9 grams more than the mean weight of babies of smokers. b. there is a 95% chance that if a woman smokes during pregnancy her baby will weigh between 76.5 grams to 486.9 grams less than if she did not smoke. c. we are 95% confident that on average, smoking causes lower birth weights of between 76.5 grams to 486.9 grams. d. this study does not suggest that there is a difference in mean birth weights when we compare smokers to nonsmokers.

Explanation:

A confidence interval gives a range of values for an unknown population parameter. Here, the 95% confidence interval for the difference in mean birth - weights (nonsmokers minus smokers) is (76.5, 486.9). This means we are 95% confident that the true difference in the population means lies within this interval. It implies that, on average, the mean weight of babies of nonsmokers is more than the mean weight of babies of smokers by an amount in this interval. We cannot say that smoking causes lower birth - weights from this observational study, just that there is a difference in means.

Answer:

A. When smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies of nonsmokers is between 76.5 grams to 486.9 grams more than the mean weight of babies of smokers.