Chapter 9, Problem R9.6RE

To determine

To calculate: Does this provided data convincing evidence to support the company’s claim.

Answer to Problem R9.6RE

There is not sufficient evidence to support the claim.

Explanation of Solution

Given information:

No of adults $\left(x\right)$ : $1000$

No of peoples got flu $\left(n\right)$ : $43$

Calculation:

So finding out the hypotheses:

  $\begin{array}{l}{H}_0:p=5\%=0.05\\ H_a=p<0.05\end{array}$

The sample proportion is the no. of successes divided by the sample size:

  $p=\frac{x}{n}=\frac{43}{1000}=0.043$

Determine the value of test statistic:

  $\begin{array}{l}z=\frac{\widehat{p}-p_o}{\sqrt{\frac{p_o\left(1-p_o\right)}{n}}}\\ z=\frac{0.043-0.05}{\sqrt{\frac{0.05\left(1-0.05\right)}{1000}}}\\ z\approx -1.02\end{array}$

The $P-$ value is the probability of obtaining the value of test statistic, or a value more extreme.

For determining the $P-$ value in table $A$ :

  $P=P\left(z<-1.02\right)=0.1539$

If the $P-$ value smaller than the significance level, reject the null hypothesis:

  $P>0.05$ , thus fails to reject the $H_0$ .