In a study of the impact of smoking on birth weight, researchers analy In a study of the impact of smoking on birth weight, researchers analy In a study of the impact of smoking on birth weight, researchers analyzed birth weights (in grams) for babies born to 189 women who gave birth in 1989 at a hospital in Massachusetts. The sample consisted of 74 women categorized as “smokers” and 115 as “non-smokers.” The difference in the two sample mean birth weights (non-smokers minus smokers) was found to be 281.7 grams. The 95% confidence interval for this difference is (76.5, 486.9) grams. This interval indicates that, with 95% confidence, the true average difference in birth weight between babies of non-smokers and smokers falls within this range. Given this information, the primary interpretation pertains to the impact of maternal smoking on birth weight, considering both the statistical significance and the magnitude of the effect. The options are as follows: Option A: "We are 95% confident that on average, smoking causes lower birth weights of between 76.5 grams to 486.9 grams." This suggests a causal relationship directly inferred from the study. However, because this is an observational study rather than a randomized controlled trial, it cannot definitively establish causality, although it indicates an association. Option 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." This is a misinterpretation of confidence intervals, as they do not provide probabilities for individual outcomes but rather for the parameter estimate in the population. Option D: "This study does not suggest that there is a difference in mean birth weights when we compare smokers to non-smokers." Given the confidence interval does not include zero and the point estimate shows a substantial difference, this statement is inconsistent with the data. Therefore, the most accurate interpretation, considering the causal implications and the statistical evidence, is: the study provides evidence of an association between maternal smoking and lower birth weights, with an estimated decrease of approximately 281.7 grams, and the true mean difference is likely between 76.5 and 486.9 grams. The phrasing in Option A suggests a causal inference that the data does not definitively establish but strongly indicates, while Options B and D misinterpret the statistical findings.
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