In order to estimate the average electric usage per month, a sample of 64 houses was selected and the electric usage was determined. Assume a population standard deviation of 320 kilowatt-hours. If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is _____ kWh.
A) 1779.6 to 1936.4
B) 1818 to 1898
C) 1792.2 to 1923.8
D) 1538 to 2178

Question

Quizplus · Accepted Answer

The 95% confidence interval for the population mean is calculated using the formula: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level (1.96 for 95%), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $1858 \pm 1.96 \frac{320}{\sqrt{64}} = 1858 \pm 1.96 \times 40 = 1858 \pm 78.4$, which gives the interval $1779.6$ to $1936.4$.

In Order to Estimate the Average Electric Usage Per Month