Question

A consumer group wants to estimate the mean electric bill for the month of December for single-family homes in St. Louis. Based on studies conducted in other cities, the standard deviation is assumed to be $31. The group wants to estimate the mean bill for December to within $7 with 97% confidence. What sample size is needed?

92

4

69

70

3

93

Answer 1

Solution :

Given that,

standard deviation =s =  $\sigma$ =$31

Margin of error = E = $7

At 97% confidence level the z is ,

$\alpha$ = 1 - 97% = 1 - 0.97= 0.03

$\alpha$ / 2 = 0.03/ 2 = 0.015

Z_$\alpha$/2 = Z_0.015 = 2.17

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = ( 2.17* 31 / 7 )²

n =92