The average natural gas bill for a random sample of 26 homes in the 19808 zip code during the month of March was $305.30 with a sample standard deviation of $46.50. The 80% confidence interval around this sample mean is ______ .
A)($293.30, $317.30)
B)($268.82, $341.78)
C)($277.94, $332.66)
D)($287.06, $323.54)

Question

Quizplus · Accepted Answer

The 80% confidence interval can be calculated using the formula for the confidence interval of the mean, which is $\bar{x} \pm Z \cdot \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $Z$ is the Z-score corresponding to the desired confidence level. For an 80% confidence level, the Z-score is approximately 1.28. Plugging in the given values: $305.30 \pm 1.28 \cdot \frac{46.50}{\sqrt{26}}$ results in the interval $(293.30, 317.30)$.

The Average Natural Gas Bill for a Random Sample of 26