Chapter 9.2, Problem 36E

To determine

To check: Whether the conditions that are required to conduct the significant test are fulfilled or not.

Answer to Problem 36E

Yes, they are fulfilled.

Explanation of Solution

Given:

Sample size ( $n$ ) is 100

Population proportion ( $p$ ) is 0.13.

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.13\\ H_a:p>0.13\end{array}$

Calculations:

Here, p be the proportion of students that walk to their elementary school.

In order to have the conduct the significance test, the following conditions must be satisfied:

  $n\times p\ge 10$

  $n\times (1-p)\ge 10$

Now, check the required conditions:

(1)

  $\begin{array}{c}n\times p=100\times 0.13\\ =13\\ >10\end{array}$

(2)

  $\begin{array}{c}n\times (1-p)=100\times (1-0.13)\\ =870\\ >10\end{array}$

From the above calculations, it is clear all the underlying conditions are satisfied. Therefore, the significance test could be conducted.