Chapter 12, Problem 42PT4

a)

To determine

To state the null and alternative hypotheses.

Answer to Problem 42PT4

  $\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1<p_2\end{array}$

Explanation of Solution

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1<p_2\end{array}$

Where, p₁ is the proportion of women who were physical active. P₂ is the proportion of women who were not physical active.

b)

To determine

To identify which inference method to be used.

Answer to Problem 42PT4

Two-sample z-test.

Explanation of Solution

Given:

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1<p_2\end{array}$

In this test, we have to compare two population proportions. Therefore, here two-sample z-test is useful.

c)

To determine

To explain whether we generalize the results to all women aged 65 and older.

Answer to Problem 42PT4

The study cannot be generalized.

Explanation of Solution

Given:

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1<p_2\end{array}$

The sample collected based on white women. Therefore, it is not a representative of all population. Hence, this result cannot be generalized to all women aged 65 and older.

d)

To determine

To explain confounding and give example of potential confounding.

Answer to Problem 42PT4

The confounding variable is Mentally stimulating activities.

Explanation of Solution

Given:

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1<p_2\end{array}$

The two variables are said to be confounded when their effects on response variable cannot be distinguished from each other. The confounding variable is Mentally stimulating activities.