Chapter 9.1, Problem 18E

(a)

To determine

To find: the conclusion would make at the $\alpha =0.01$ level.

Answer to Problem 18E

There is enough convincing evidence that the percentage of teens in the school that say they seldom or never argue with their friends is different from 72%.

Explanation of Solution

Given:

  $\begin{array}{l}P=0.0291=2.91\%\\ \alpha =0.01\end{array}$

Given claim is proportion is 72%.

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

  $\begin{array}{l}{H}_0:p=72\%=0.72\\ H_1:p\ne 0.72\end{array}$

If the P-value is smaller than the significance level $\alpha$ , then reject the null hypothesis:

  $0.0291<0.01\Rightarrow \text{Fail to reject }{H}_0$

There is enough convincing evidence that the percentage of teens in the school that say they seldom or never argue with their friends is different from 72%.

(b)

To determine

To Explain: the conclusion from part (a) change if a 5% significance level was used intead.

Answer to Problem 18E

Yes

There is sufficient convincing evidence that the percentage of teens in the school that say they seldom or never argue with their friends is different from 72%.

Explanation of Solution

Given:

  $\begin{array}{l}P=0.0291=2.91\%\\ \alpha =0.01\end{array}$

Given claim is proportion is 72%.

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

  $\begin{array}{l}{H}_0:p=72\%=0.72\\ H_1:p\ne 0.72\end{array}$

If the P-value is smaller than the significance level $\alpha$ , then reject the null hypothesis:

  $0.0291<0.01\Rightarrow \text{Fail to reject }{H}_0$

There is sufficient convincing evidence that the percentage of teens in the school that say they seldom or never argue with their friends is different from 72%.

It is observed that the conclusion has changed.