Question

Banking fees have received much attention during the recent economic recession as banks look for ways to recover from the crisis. A sample of 32 customers paid an average fee of ​$12.33 per month on their​ interest-bearing checking accounts. Assume the population standard deviation is ​$1.75. Complete parts a and b below. a. Construct a 95​% confidence interval to estimate the average fee for the population. The 95​% confidence interval has a lower limit of ​$ nothing and an upper limit of ​$ nothing. ​(Round to the nearest cent as​ needed.) b. What is the margin of error for this​ interval? ​$ nothing ​(Round to the nearest cent as​ needed.)

Answer 1

Solution :

Given that,

= $12.33

= $1.75

n = 32

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

=1.96 * (1.75 / 32)

= 0.6

At 99% confidence interval estimate of the population mean is,

- E < < + E

12.33 - 0.6 < < 12.33 + 0.6

11.73< < 12.93

lower limit = $11.7 , upper limit $ 12.9

margin of error =$ 0.6