Chapter 9.2, Problem 36E

To determine

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

Answer to Problem 36E

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

Explanation of Solution

Given Information:

  $\text{Sample}\text{size}(n)=200$ .

  $\text{Population}\text{proportion}\left(p\right)=0.99$ .

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

  $\begin{array}{c}\text{Number}\text{of}\text{success}=np\\ =200\times 0.99\\ =198\end{array}$

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

  $\begin{array}{c}\text{Number}\text{of}\text{failur}e=n\left(1-p\right)\\ =200\times \left(1-0.99\right)\\ =2\end{array}$

The number of success is greater than 10 but the number of failure is less than 10.

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