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Question

Is it true that an apple a day keeps the doctor away? A study designed and conducted by the National Health and Nutrition Examination Study (results published in the Journal of the American Medical Association) considered 8,399 American adults of whom 756 reported that they ate a small apple a day. The rest did not eat apples or ate them infrequently. The number of healthcare visits in the previous 36 months was recorded. Conduct a test to determine whether the adage is true.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 14Let's define the following:

- $n_1=756$ - is the sample size or the number of randomly selected American adults who ate a small apple a day
- $n_2=7643$ - is the sample size or the number of randomly selected American adults who don't eat an apple a day
- $\bar{x}_1$ - is the sample mean or the mean number of healthcare visits of $756$ American adults who ate a small apple a day
- $\bar{x}_2$ - is the sample mean or the number of healthcare visits of $7643$ American adults don't eat an apple a day
- $s_1^2$ - is the sample variance or the variance of the number of healthcare visits of $756$ American adults who ate a small apple a day
- $s_2^2$ - is the sample variance or the variance of the number of healthcare visits of $7643$ American adults don't eat an apple a day
- $ν_1=ν_2=\infty$ are the number of degrees of freedom by Sample $1$ and Sample $2$
- $\alpha=0.05$ - is the level of significance

Our goal for this part of the problem is to determine whether eating an apple a day decreases the number of healthcare visits of American adults.

*How can we identify whether to apply equal or unequal variances t-tests?*

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