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 31 customers paid an average fee of $12.27

per month on their​ interest-bearing checking accounts. Assume the population standard deviation is $1.82.

Construct a 90% confidence interval to estimate the average fee for the population.

The 90​% confidence interval has a lower limit of ​A.$____ and an upper limit of B.$______

a?

b?

Answer 1

Solution :

Given that,

= $12.27

= $1.82

n = 31

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 * ( 1.82/ 31)

= 0.5377

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

- E < < + E

12.27 - 0.5377 < < 12.27 + 0.5377

11.7323< < 12.8077

lower limit = 11.7323

upper limit = 12.8077