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 39 customers paid an average fee of ​$12.08 per month on their​ interest-bearing checking accounts. Assume the population standard deviation is ​$1.79 . Complete parts a and b below. a. Construct a 90 ​% confidence interval to estimate the average fee for the population. The 90 ​% confidence interval has a lower limit of ​$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,

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (1.79 / 39 )

= 0.47

At 90% confidence interval estimate of the population mean is,

- E < < + E

12.08 - 0.47 < < 12.08 + 0.47

11.61 < < 12.55

a)

The 90 ​% confidence interval has a lower limit of $11.61.

The 90 ​% confidence interval has a upper limit of $ 12.55

b)

The margin of error for this​ interval is $0.47.