Chapter 20, Problem 20E

To determine

To test an appropriate hypothesis and state your conclusion and be sure the appropriate assumptions and conditions are satisfied before you proceed.

Answer to Problem 20E

All the conditions are not met.

Explanation of Solution

It is given in the question that an appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment retail stores. The company goal is to keep the level of damaged machines below $2\%$ . They want to test the claim that is this strong evidence that the warehouse is failing to meet the company goal. Thus, the null hypothesis states that the level of damaged machine is equal to $2\%$ . And the alternative hypothesis states that the level of damaged machine is more than $2\%$ . So, we define hypothesis as:

  $\begin{array}{l}{H}_0:p=0.02\\ H_a:p>0.02\end{array}$

Thus, let us check the appropriate conditions and assumptions for inference to proceed further to test hypothesis as:

Random condition: It is satisfied as the sample was randomly selected from the population.

Independent condition: It is satisfied as we can assume that the sample is independent.

  $10\%$ condition: It is satisfied as the sample is less than $10\%$ of all population.

Success/failure condition: It is not satisfied because both are not greater than ten as,

  $\begin{array}{l}np=0.02(60)<10\\ n(1-p)=0.98(60)>10\end{array}$

Thus, all the conditions are not satisfied, so we cannot proceed further for testing hypothesis for the claim.