Chapter 9, Problem 4CRE

a.

To determine

To check: Whether the sufficient evidences are provided the data to support the claim of the company.

Answer to Problem 4CRE

No

Explanation of Solution

Given:

  $\begin{array}{l}\text{Number of trials}\left(n\right)=1000\\ \text{Number of success}\left(x\right)=43\\ \text{Population proportion}\left(p\right)=0.05\end{array}$

Formula used:

The formula to compute the test statistic is:

  $z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}$

Calculation:

Using the information, the null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.05\\ H_a:p<0.05\end{array}$

Using the Ti-83 calculator the output is:

  

Decision rule:

The p-value is more than the significance level. Thus, decision is written as the non-rejection of the null hypothesis.

Conclusion:

At 5% significance level, there are sufficient evidence to support the provided claim.

b.

To determine

To find: The error that has been committed.

Answer to Problem 4CRE

Type II error.

Explanation of Solution

From above part, the null hypothesis has not been rejected. Thus, there is a possibility of committing the Type II error.

c.

To determine

To find: Whether the Type I error or Type II error is more serious from the point of view of the company.

Answer to Problem 4CRE

Type I error

Explanation of Solution

Due to the Type I error it is possible that more people are getting flu than the test has been indicated.

Thus, type I error is more serious.