Chapter 25, Problem 14E

To determine

To test an appropriate hypothesis to see if there is evidence that either of these sites has a higher average wind speed.

Answer to Problem 14E

There is sufficient evidence to support the claim that one of these sites has a higher average wind speed.

Explanation of Solution

It is given from the previous question that:

  $n=1114$

Now, the sample mean of the difference will be then,

  $\overline{d}=0.204$

Now the standard deviation of the difference will be then,

  $s_d=2.551$

Now, let us define the hypotheses as:

  $\begin{array}{l}{H}_0:{\mu }_d=0\\ H_a:{\mu }_d>0\end{array}$

Thus, the value of test statistics will be as:

  $\begin{array}{l}t=\frac{\overline{d}}{s_d/\sqrt{n}}\\ =\frac{0.204}{2.551/\sqrt{1114}}\\ =2.669\end{array}$

The degree of freedom will be as:

  $\begin{array}{l}df=n-1\\ =1114-1\\ =1113>1000\end{array}$

Thus, the P-value will be as:

  $P<0.005$

As we know if the P-value is less than the significance level then reject the null hypothesis. Thus, we have,

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

Thus, we conclude that there is sufficient evidence to support the claim that one of these sites has a higher average wind speed.