Chapter PVI, Problem 29RE

(a)

To determine

To explain is there strong evidence that IRS risk is different in people who frequently consume dairy products than in those who do not.

Answer to Problem 29RE

These data suggest the IRS risk is different in two groups and it appears people who consume dairy products often have a lower risk, on average.

Explanation of Solution

It is given in the question that a study published I the Journal of the American medical association examined people to see if they showed any signs of IRS involving major risk factors for Type II diabetes and heart disease. Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator $\text{TI}-89$ . Then select $6:2-$ PropZTestfrom the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded. So, the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p_{\text{High}}-p_{\text{Low}}=0\\ H_a:p_{\text{High}}-p_{\text{Low}}\ne 0\end{array}$

  $\begin{array}{l}{x}_1=24\\ n_1=102\\ x_2=85\\ n_2=190\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}z=-3.57\\ P=0.0004\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P<0.05\Rightarrow \text{Reject }{H}_0$

Thus, we conclude that these data suggest the IRS risk is different in two groups and it appears people who consume dairy products often have a lower risk, on average.

(b)

To determine

To explain does this indicate that diary consumption influences the development of IRS.

Answer to Problem 29RE

No, this does not indicate that diary consumption influences the development of IRS.

Explanation of Solution

It is given in the question that a study published I the Journal of the American medical association examined people to see if they showed any signs of IRS involving major risk factors for Type II diabetes and heart disease. And these data suggest the IRS risk is different in two groups and it appears people who consume dairy products often have a lower risk, on average. Thus, this does not indicate that diary consumption influences the development of IRS because it does not indicate causality as this is not an experiment.