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In 2000, the Journal of the American Medical Association (JAMA) published a study that examined pregnancies that resulted in the birth of twins. Births were classified as preterm with intervention (induced labour or caesarean), preterm without procedures, or term/ post-term . Researcher s also classified the pregnancies by the level of prenatal medical care the mother received (inadequate, adequate , or intensive). The data, from the years 1995-1997, are summarized in the table on the next page. Figures are in thousands of births.

In 2000, the Journal of the American Medical Association (JAMA) published a study that examined pregnancies that resulted in the birth of twins. Births were classified as preterm with intervention (induced labor or cesarean), preterm without procedures, or term/post-term. Researchers also classified the pregnancies by the level of prenatal medical care the mother received (inadequate, adequate, or intensive). The data, from the years 1995-1997, are summarized in the table below. Figures are in thousands of births.

\begin{array}{l|ccc|r} \begin{array}{c} \text { Level of } \\ \text { Prenatal } \\ \text { Care) } \end{array}& \begin{array}{c} \text { Preterm } \\ \text { (induced or } \\ \text { cesarean) } \end{array} & \begin{array}{c} \text { Preterm } \\ \text { (without } \\ \text { procedures) } \end{array} & \begin{array}{c} \text { Term or } \\ \text { Post-Term } \end{array} & \text { Total } \\ \hline \text { Intensive } & 18 & 15 & 28 & \mathbf{61} \\ \text { Adequate } & 46 & 43 & 65 & \mathbf{154} \\ \text { Inadequate } & 12 & 13 & 38 & \mathbf{63} \\ \hline \text { Total } & \mathbf{76} & \mathbf{71} & \mathbf{131} & \mathbf{278} \end{array}

What percent of these mothers received inadequate medical care during their pregnancies?

Draw a correctly labeled graph showing the demand for apples. On your graph, illustrate what happens to the demand for apples if a new report from the Surgeon General finds that an apple a day really does keep the doctor away.

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

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Let'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