Chapter 9.2, Problem 37E

To determine

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

Answer to Problem 37E

No, they are not fulfilled.

Explanation of Solution

Given:

Sample size ( $n$ ) is 10

Population proportion ( $p$ ) is 0.50.

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.50\\ H_a:p\ne 0.50\end{array}$

Calculations:

Here, p be the proportion of coins that land head.

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)

  $\begin{array}{c}n\times p=10\times 0.5\\ =5\\ <10\end{array}$

(2)

  $\begin{array}{c}n\times (1-p)=10\times (1-0.5)\\ =5\\ <10\end{array}$

From the above calculations, it is clear all the underlying conditions are not satisfied. Therefore, the significance test cannot be conducted.