Chapter 24, Problem 16E

(a)

To determine

To state the null and alternative hypotheses for this test.

Answer to Problem 16E

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_1:{\mu }_1\ne {\mu }_2\end{array}$

Explanation of Solution

In this question, the data is collected from the water of streams about the pH level and the substrate. The boxplot of the same is given. Thus, the null hypothesis states that the mean of both groups are equal and the alternative hypothesis states that the claim of a difference.

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_1:{\mu }_1\ne {\mu }_2\end{array}$

(b)

To determine

To explain do the assumptions and conditions appear to be met.

Answer to Problem 16E

All conditions are met.

Explanation of Solution

In this question, the data is collected from the water of streams about the pH level and the substrate. The boxplot of the same is given. Thus, the conditions to be satisfied are:

Random condition: It is satisfied because we assume that the samples of water from streams were randomly selected.

Independent condition: It is satisfied because we assume that the streams with different types of rocks do not have the same water source.

Normal condition: It is satisfied because the degrees of freedom are $133$ , which indicate large samples and the central limit theorem then tells us that the sampling distribution of the sample mean is approximately normal.

(c)

To determine

To find out what conclusion would you draw.

Answer to Problem 16E

There is sufficient evidence to support the claim of a difference.

Explanation of Solution

In this question, the data is collected from the water of streams about the pH level and the substrate. The boxplot of the same is given. It is given that the P-value is:

  $P<0.0001$

And we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected. Thus,

  $P<0.05\Rightarrow \text{Reject }{H}_0$

Thus, we conclude that there is sufficient evidence to support the claim of a difference.