Questions: Find a 94% confidence interval for μd. Let μd=μ1-μ2, where μ1 is the mean solar energy generated for the east-west highways and μ2 is the mean solar energy generated for the north-south highways. (Round to one decimal place as needed.)

Solution Steps

The mean solar energy generated for the east-west highways is calculated as follows:

\[ \mu_1 = \frac{\sum_{i=1}^N x_i}{N} = \frac{37184}{5} = 7436.8 \]

The mean solar energy generated for the north-south highways is calculated as follows:

\[ \mu_2 = \frac{\sum_{i=1}^N x_i}{N} = \frac{38623}{5} = 7724.6 \]

The variance and standard deviation for the east-west highways are calculated as follows:

\[ \sigma_1^2 = \frac{\sum (x_i - \mu_1)^2}{n-1} = 2192174.7 \] \[ \sigma_1 = \sqrt{2192174.7} = 1480.6 \]

The variance and standard deviation for the north-south highways are calculated as follows:

\[ \sigma_2^2 = \frac{\sum (x_i - \mu_2)^2}{n-1} = 2391119.3 \] \[ \sigma_2 = \sqrt{2391119.3} = 1546.3 \]

The confidence interval for the difference between the two population means is calculated using the formula:

\[ (\bar{x}_1 - \bar{x}_2) \pm t \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \]

Substituting the values:

\[ 7436.8 - 7724.6 \pm 2.2 \cdot \sqrt{\frac{1480.6^2}{5} + \frac{1546.3^2}{5}} \]

Calculating the confidence interval gives:

\[ (-2384.4, 1808.8) \]

Final Answer