Chapter 9.1, Problem 7E

a.

To determine

The stated hypotheses are correct or not is to be described and if not write down the correct hypotheses.

Answer to Problem 7E

The correct hypotheses are listed as:

  $\begin{array}{l}{H}_0:\text{}p=0.37\\ H_a:\text{}p>0.37\end{array}$

Explanation of Solution

Given that:

The null hypothesis given by the following expression:

  $H_0:\text{}\widehat{p}=0.37$

And the alternate hypothesis is given by the following expression:

  $H_a:\text{}\widehat{p}\ne 0.37$

Now, know that the hypotheses always used the population value not the sample value. So the sample values stated in the null hypothesis and alternate hypothesis should be remove and replaced by population value.

The correct hypotheses are listed as:

  $\begin{array}{l}{H}_0:\text{}p=0.37\\ H_a:\text{}p>0.37\end{array}$

Conclusion:

Hence, there is use population value not the sample value in hypotheses.

b.

To determine

The stated hypotheses by the doctor are correct or not is to be described and if not write down the correct hypotheses.

Answer to Problem 7E

The correct hypotheses are listed as:

  $\begin{array}{l}{H}_0:\text{}p=0.3000grams\\ H_a:\text{}p<0.3000grams\end{array}$

Explanation of Solution

Given that:

The null hypothesis given by the following expression:

  $H_0:\text{}\overline{x}=0.3000grams$

And the alternate hypothesis is given by the following expression:

  $H_a:\text{}\overline{x}<0.3000grams$

Now, know that the hypotheses always used the population value not the mean value. So the sample values stated in the null hypothesis and alternate hypothesis should be remove and replaced by population value.

The correct hypotheses are listed as:

  $\begin{array}{l}{H}_0:\text{}p=0.3000grams\\ H_a:\text{}p<0.3000grams\end{array}$

Conclusion:

Hence, there is use population value not the sample value in hypotheses.