Chapter 9.2, Problem 33E

To determine

Whether the statement satisfied the conditions for one sample z test for the population proportion p.

Answer to Problem 33E

All three conditions are satisfied.

Explanation of Solution

Given Information:

  $\text{Sample}\text{size}(n)=100$ .

  $\text{Probability}(p)=12\%$

Formula Used:

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

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

Population proportion is 12%.

Convert 12% into decimal.

  $\frac{12}{100}=0.12$

Three conditions that needs to satisfy are Random, Normal, Independent.

Since the samples are taken randomly. Thus, the condition of random is satisfied.

Now, find the number of success. Use the formula $\text{Number}\text{of}\text{success}=np$ .

  $\begin{array}{c}\text{Number}\text{of}\text{success}=np\\ =100\times 0.12\\ =12\end{array}$

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

  $\begin{array}{c}\text{Number}\text{of}\text{failur}e=n\left(1-p\right)\\ =100\times \left(1-0.12\right)\\ =88\end{array}$

Both failure and success are greater than 10. Thus normal condition is satisfied.

Independent condition is also satisfied because the sample size is less than 10% of the population size.

Hence, all three conditions are satisfied.