A local public health clinic is interested in promoting their new program at red
ID: 3266354 • Letter: A
Question
A local public health clinic is interested in promoting their new program at reducing the average number of cigarettes smoked per day. Suppose they decide to conduct a matched study where smokers enrolled in the study are paired with smokers without the intervention on a number of characteristics so as to ensure independent samples. The study consisted of a SRS of 167 participants in each arm. The following table represents the summary statistics for the analysis.
Without knowing that the SRS constitutes a normal distribution, what theorem lets us know we can go ahead with the approximation?
Study Am Average cigarettes smoked/day Standard deviation Intervention Control 3.1 2.9 17Explanation / Answer
The central limit theorem let us know that we can go ahead with the approximation as it states that the sampling distribution of the mean of any independent,random variable will be normal or nearly normal, if the sample size is large enough.
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