Chapter 20, Problem 11E

(a)

To determine

To write appropriate hypotheses.

Answer to Problem 11E

  $\begin{array}{l}{H}_0:p=0.3\\ H_a:p>0.3\end{array}$

Explanation of Solution

It is given in the question that only about $30\%$ of the wells that are drilled find adequate water at a depth of $100$ or less. Thus, the null hypothesis states that the percentage of the wells that are drilled find adequate water is equal to $30\%$ and the alternative hypothesis is that the percentage of the wells that are drilled find adequate water is greater than $30\%$ . So, we have,

  $\begin{array}{l}{H}_0:p=0.3\\ H_a:p>0.3\end{array}$

(b)

To determine

To check the necessary assumptions.

Explanation of Solution

It is given in the question that only about $30\%$ of the wells that are drilled find adequate water at a depth of $100$ or less. And the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p=0.3\\ H_a:p>0.3\end{array}$

Thus, let us check the necessary assumptions as:

Random condition: It is possibly a simple random sample.

  $10\%$ condition: We do not know if the sample is less than $10\%$ of his customers but could be viewed as less than $10\%$ of all possible customers.

Success/failure condition: It is greater than ten,

  $\begin{array}{l}np=0.3(80)>10\\ n(1-p)=0.7(80)>10\end{array}$

Thus, all the conditions are met expect the $10\%$ condition.

(c)

To determine

To find out what is the P-value.

Answer to Problem 11E

  $P-\text{value}=0.232$ .

Explanation of Solution

It is given in the question that only about $30\%$ of the wells that are drilled find adequate water at a depth of $100$ or less. And the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p=0.3\\ H_a:p>0.3\end{array}$

Thus, by using the $1-\text{PropZInt}$ test function of graphing utility, we will calculate the P-value and test statistic value, thus, we have,

  $\begin{array}{l}z=0.73\\ P-\text{value}=0.232\end{array}$

(d)

To determine

To explain what P-value means in this context.

Explanation of Solution

It is given in the question that only about $30\%$ of the wells that are drilled find adequate water at a depth of $100$ or less. And the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p=0.3\\ H_a:p>0.3\end{array}$

  $P-\text{value}=0.232$

Thus, we can say that if his dowsing is no different from standard methods, there is more than a $23\%$ chance of seeing results as good as those of the dowsers, or better, by natural sampling variation.

(e)

To determine

To find out what is the conclusion.

Explanation of Solution

It is given in the question that only about $30\%$ of the wells that are drilled find adequate water at a depth of $100$ or less. And the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p=0.3\\ H_a:p>0.3\end{array}$

  $P-\text{value}=0.232$

Thus, the P-value is greater than $0.05$ . So, we can conclude that we will fail to reject that the dowser's chance of findingwater is the same as normal drilling.