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 34customers paid an average fee of $12.23

per month on their interest-bearing checking accounts. Assume the population standard deviation is

$1.671.67.

Complete parts a and b below.

a. Construct a9 5% confidence interval to estimate the average fee for the population.The 95% confidence interval has a lower limit of$_____and an upper limit of$____

(Round to the nearest cent as needed.)

b. What is the margin of error for this interval?

(Round to the nearest cent as needed.)

Answer #1

Solution :

Given that,

Point estimate = sample mean = = 12. 23

Population standard deviation = = 1.67

Sample size = n = 34

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* ( 1.67 / 34)

= 0.561

At 95% confidence interval estimate of the population mean is,

- E < < + E

12. 23- 0.561 < < 12.23 + 0.561

11. 669< < 12.791

(11. 67, 12.79 )

The 99% confidence level has a lower limit of $11.67 and an upper limit of $12.79

b)

The margin error for this interval is =0.561

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