Chapter 9.1, Problem 11E

To determine

To Explain: the P-value.

Answer to Problem 11E

There is a 5.89% possibility that the mean volume of liquid in a sample of 40 bottles is 179.6 millilitres or more extreme, when the mean volume of liquid of all bottles is 180 millilitres

Explanation of Solution

Given:

  $\begin{array}{l}P=0.0589=5.89\%\\ \overline{x}=179.6\\ s=1.3\end{array}$

Claim is mean is 180.

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.

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

The P-value is the probability of getting the value of the test static or a value more extreme, when the null hypothesis is true.

There is a 5.89% possibility that the mean volume of liquid in a sample of 40 bottles is 179.6 millilitres or more extreme, when the mean volume of liquid of all bottles is 180 millilitres