A consumer group would like to estimate the mean monthly electricity charge for a single family house in July (within $5) using a 99 percent level of confidence. Based on similar studies the standard deviation is estimated to be $20.00. How large a sample is required?
A) 105
B) 106
C) 107
D) 108
E) 109

Question

Quizplus · Accepted Answer

The formula to calculate the sample size required to estimate the population mean with a specified level of confidence is:

n = [Z*(σ / E)]^2

where:
Z = the Z-value for the desired level of confidence (in this case, Z = 2.576 for a 99% level of confidence)
σ = the population standard deviation (estimated as $20 in this case)
E = the maximum error of the estimate (in this case, $5)

Substituting the given values, we get:

n = [2.576*(20/5)]^2 = [2.576*4]^2 = 10.304^2 = 106.07

Since we cannot have a fraction of a person for the sample size, we round up to the nearest whole number and get:

n = 107

Therefore, the best choice is option (C) 107.

A Consumer Group Would Like to Estimate the Mean Monthly