Chapter 20, Problem 9E

To determine

To explain how many mistakes can you find.

Explanation of Solution

It is given in the question that many people have trouble setting up all the feature of their cell phones, so the company has developed what it hopes will be easier instructions. The company tests the new system on $200$ people, of whom $188$ were successful. Thus, the test was conducted to find out is this strong evidence that the new system fails to meet the company’s goal. Thus, the mistakes in the output were that we should have use p instead of using $\widehat{p}$ in the hypothesis defined. And also the question was about failing to meet the goal so, the alternative hypothesis should be $p<0.96$ . In this test, the $10\%$ condition was not checked and the success/failure condition was not met as,

  $np=0.04(200)=8<10$

Also, in the calculation the correct calculation was:

  $\begin{array}{l}\frac{188}{200}=0.94\\ SD=\sqrt{\frac{0.96(0.04)}{200}}\\ =0.014\\ z=\frac{0.94-0.96}{0.014}\\ =-1.43\\ P(z<-1.43)=0.076\end{array}$

So, we can say, there is only weak evidence that the new instructions do not work.