Question

Solar energy generation along highways. Refer to the International Journal of Energy and Environmental Engineering (December 2013) study of solar energy generation along highways, Exercise 8.39 (p. 481). Recall that the researchers compared the mean monthly amount of solar energy generated by east-west– and north-south– oriented solar panels using a matched-pairs experiment. However, a small sample of only five months was used for the analysis. How many more months would need to be selected to estimate the difference in means to within 25 kilowatt-hours with a 90% confidence interval? Use the information provided in the SOLAR file to find an estimate of the standard error required to carry out the calculation

Short answer

28 months would need to estimate the difference in means to within 25 kilowatt hours.

Step-by-step solution

Given Information

With a 90% confidence interval, the researchers compared the mean monthly amount of solar energy.

The standard error is 86.4.

The sampling error is 25.

Z-value

A minimum of two steps are required.

For $\alpha =0.1$

The z-value is given by

$$\begin{gathered} z_{\frac{\alpha }{2}}=z_{0.05} \\ =1.645 \end{gathered}$$

Compute the sample

For, $z=1.645, andSE=86.4$

The sample is calculated as

$$\begin{gathered} n_d={\left\{\frac{z_{\frac{\alpha }{2}}\left({\sigma }_d\right)}{SE}\right\}}^2 \\ ={\left\{\frac{1.645\times 86.4}{25}\right\}}^2 \\ ={\left\{\frac{142.128}{25}\right\}}^2 \\ ={\left\{5.685\right\}}^2 \\ =32.319 \\ =33 \end{gathered}$$

A small sample of only 5 months used for analysis.

Therefore,

$33-5=28$

Therefore, 28 months would need to estimate the difference in means to within 25 kilowatt hours.