Chapter 9.1, Problem 17E

(a)

To determine

To find: the conclusion would make at the $\alpha =0.10$ level.

Answer to Problem 17E

There is sufficient convincing evidence that the correct mean volume of liquid is different from 180 millilitres.

Explanation of Solution

Given:

  $\begin{array}{l}P=0.0589\\ \alpha =0.10\end{array}$

Given claim is mean is 180

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.

  $\begin{array}{l}{H}_0:\mu =180\\ H_1:\mu \ne 180\end{array}$

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

  $0.0589<0.10\Rightarrow \text{Reject }{H}_0$

There is sufficient convincing evidence that the correct mean volume of liquid is different from 180 millilitres.

(b)

To determine

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

Answer to Problem 17E

Yes

There is enough convincing evidence that the true mean volume of liquid is different from 180 millilitres.

Explanation of Solution

Given:

  $\begin{array}{l}P=0.0589\\ \alpha =0.10\end{array}$

Given claim of mean is 180.

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.

  $\begin{array}{l}{H}_0:\mu =180\\ H_1:\mu \ne 180\end{array}$

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

  $0.0589<0.10\Rightarrow \text{Reject }{H}_0$

There is enough convincing evidence that the true mean volume of liquid is different from 180 millilitres.

It is observed that the conclusion changed.