Chapter 9.2, Problem 51E

To determine

To find: Whether there are sufficient evidence to show that the claim of DMC is incorrect at 5% significance level.

Answer to Problem 51E

There is sufficient evidence to show that the claim of DMC is incorrect at 5% significance level.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Hypothesized proportion}\left(p_0\right)=60\%=0.60\\ \text{Sample size}\left(n\right)=125\\ \text{Sample proportion}\left(\widehat{p}\right)=\frac{x}{n}=\frac{86}{125}=0.688\end{array}$

Formula used:

The test statistic formula for testing the proportion is:

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

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.60\\ H_a:p\ne 0.60\end{array}$

The obtained Minitab output is:

  

The p -value is 0.045.

Here, $p\text{-value}\left(0.045\right)<\alpha \left(0.05\right)$ . The null hypothesis is rejected.

Conclusion:

There is sufficient evidence to show that the claim of DMC is incorrect at 5% significance level.