Chapter 20, Problem 19E

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 19E

All the conditions are not met.

Explanation of Solution

It is given in the question that a company with a fleet of $150$ cars found that the emissions of $7\text{ out of the 22}$ they tested failed to meet pollution control guidelines. They want to test that is this strong evidence that more than $20\%$ of the fleet might be out of compliance. Thus, the null hypothesis states that the fleet might be out of compliance is equal to $20\%$ . And the alternative hypothesis states that the fleet might be out of compliance is more than $20\%$ . So, we define hypothesis as:

  $\begin{array}{l}{H}_0:p=0.20\\ H_a:p>0.20\end{array}$

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

Random condition: It is satisfied as we have assumed that 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,

  $\begin{array}{l}np=0.20(22)<10\\ n(1-p)=0.80(22)>10\end{array}$

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