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c. Smoking is associated with lower birth weights. When smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies born to nonsmokers will be between 76.5 grams to 486.9 grams more than the mean birth weight of babies born to smokers.
Step-by-step explanation:
The difference in mean birth weights (nonsmokers minus smokers) is 281.7 grams with a margin of error of 205.2 grams with 95% confidence.
Then, we know that the 95% confidence interval is (76.5, 486.9)
<em>a. We are 95% confident that smoking causes lower birth weights by an average of between 76.5 grams to 486.9 grams.</em>
False, it interprets the confidence interval as a probability for individual cases. The confidence interval is a range for the population mean.
<em>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.</em>
False, it interprets the confidence interval as a probability for individual cases. The confidence interval is a range for the population mean.
<em>c. Smoking is associated with lower birth weights. When smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies born to nonsmokers will be between 76.5 grams to 486.9 grams more than the mean birth weight of babies born to smokers.</em>
True.
<em>d. With such a large margin of error, this study does not suggest that there is a difference in mean birth weights when we compare smokers to nonsmokers.</em>
There is enough evidence, as the lower bound of the confidence is positive. This means that there is only a probability of 0.05/2=0.025 that the true mean weight difference is smaller than 76.5 grams.