Chapter 9.2, Problem 35E

To determine

The reason whether the carry out a one sample z test for the population proportion is safe or not.

Answer to Problem 35E

It is not safe to carry a one sample z test for the population proportion.

Explanation of Solution

Given Information:

  $\text{Sample}\text{size}(n)=10$ .

  $H_o:p=0.5$ .

Formula Used:

  $\text{Number}\text{of}\text{success}=np$ .

  $\text{Number}\text{of}\text{failur}e=n\left(1-p\right)$.

Find the number of success. Use the formula $\text{Number}\text{of}\text{success}=np$ .

  $\begin{array}{c}\text{Number}\text{of}\text{success}=np\\ =10\times 0.5\\ =5\end{array}$

Similarly, find the number of failure. Use the formula $\text{Number}\text{of}\text{failur}e=n\left(1-p\right)$ .

  $\begin{array}{c}\text{Number}\text{of}\text{failur}e=n\left(1-p\right)\\ =10\times \left(1-0.5\right)\\ =5\end{array}$

Since, both failure and success are less than 10. Thus,it is not safe to carry a one sample z test for the population proportion.

Hence, it is not safe to carry a one sample z test for the population proportion.