Chapter 9.1, Problem 21E

(a)

To determine

To Explain: the appropriate hypothesis

Answer to Problem 21E

  $H_0:\mu =1$

  $H_1:\mu <1$

Explanation of Solution

Given:

Claim is mean is less than 1 pound

The null hypothesis statement is that the population value is equal to the value given in the claim:

  $H_0:\mu =1$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population mean 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.

  $H_1:\mu <1$

  $\mu$ is the mean weight of all bread loaves made by the bakery.

(b)

To determine

To find: the reason there is some proof for the alternative hypothesis.

Answer to Problem 21E

There is some proof for the alternative hypothesis, the reason that the sample mean of 0.975 pound is less than 1 pound and corresponds with the claim of the alternative hypothesis that the mean is less than 1 pound.

Explanation of Solution

Given:

  $\overline{x}=0.975$

Claim is mean is less than 1

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population mean 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

  $\begin{array}{l}{H}_0:\mu =1\\ H_1:\mu <1\end{array}$

There is some proof for the alternative hypothesis, the reason that the sample mean of 0.975 pound is less than 1 pound and corresponds with the claim of the alternative hypothesis that the mean is less than 1 pound.

(c)

To determine

To Explain: the P-value.

Answer to Problem 21E

Here 8.06% possibility that the mean weight of a simple random sample of bread loaves which is 0.975 pound or more extreme, when the mean weight of all bread loaves is actually one pound.

Explanation of Solution

Given:

  $\begin{array}{l}\overline{x}=0.975\\ P=0.0806=8.06\%\end{array}$

Given claim is mean is less than 1.

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

  $\begin{array}{l}{H}_0:\mu =1\\ H_1:\mu <1\end{array}$

The P-value is the probability of getting the sample results, or more extreme, when the null hypothesis is true.

Here 8.06% possibility that the mean weight of a simple random sample of bread loaves which is 0.975 pound or more extreme, when the mean weight of all bread loaves is actually one pound.

(d)

To determine

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

Answer to Problem 21E

There is no convincing proof that the mean weight of all bread loaves is less than 1 pound.

Explanation of Solution

Given:

  $\begin{array}{l}\overline{x}=0.975\\ P=0.0806=8.06\%\\ \alpha =0.01\end{array}$

Claim is mean is less than 1.

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

  $\begin{array}{l}{H}_0:\mu =1\\ H_1:\mu <1\end{array}$

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

  $0.0806>0.01\Rightarrow \text{Fail to eject }{H}_0$

There is no convincing proof that the mean weight of all bread loaves is less than 1 pound.