Exhibit 8-4
In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was determined. Assume a population standard deviation of 450-kilowatt hours.
-Refer to Exhibit 8-4. If the sample mean is 1,858 KWH, the 95% confidence interval estimate of the population mean is
A)1,760 to 1,956 KWH
B)1,858 to 1,956 KWH
C)1,760 to 1,858 KWH
D)none of these alternatives is correct

Question

Quizplus · Accepted Answer

A 95% confidence interval estimate can be found using the formula:

(sample mean) +/- (critical value) * (standard error)

The critical value for a 95% confidence interval with 80 degrees of freedom (81-1) is 1.990. The standard error can be found using the formula:

standard error = (population standard deviation) / sqrt(sample size)
standard error = 450 / sqrt(81)
standard error = 50

Plugging in the values, we get:

1,858 +/- 1.990 * 50
1,858 +/- 99.5

So the 95% confidence interval is 1,858 - 99.5 to 1,858 + 99.5, or 1,760 to 1,956. Therefore, the best choice is A.

Exhibit 8-4 In Order to Estimate the Average Electric Usage Per Month