Chapter 9.2, Problem 38E

To determine

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

Answer to Problem 38E

Yes, they are fulfilled.

Explanation of Solution

Given:

Sample size ( $n$ ) is 200

Population proportion ( $p$ ) is $\frac{2}{3}$ .

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=\frac{2}{3}\\ H_a:p>\frac{2}{3}\end{array}$

Calculation:

Here, p be the proportion of alumni of college that are favor of firing the coach.

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

  1. $n\times p\ge 10$

  2. $n\times (1-p)\ge 10$

Now, check the required conditions:

(1)

  $\begin{array}{c}n\times p=200\times \frac{2}{3}\\ =133.333\\ >10\end{array}$

(2)

  $\begin{array}{c}n\times (1-p)=200\times \left(1-\frac{2}{3}\right)\\ =66.667\\ >10\end{array}$

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