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 38 customers paid an average fee of $12.79 per month on their​ interest-bearing checking accounts. Assume the population standard deviation is ​$1.92. 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 $____ 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

c) We want to find 95% confidence interval for population mean 

Since the population standard deviation() is given, so we need to use critical z value to obtained the confidence interval.

The formula of confidence interval for population mean () is as follow:


Where E is the margin of error

the formula of margin of error is as follows:

Let's find the value of Z_c, for confidence level = c = 0.95

The level of significance = = 1 - c =1 - 0.95 = 0.05

Therefore, 1- /2 =1- 0.05 /2 = 1- 0.025 = 0.9750

The z value corresponding to the probability = 0.9750 is 1.96

Look the following image:

So we have, Z_c = 1.96, , n = 38, = 1.92

Plug these values in the formula of E, we get

Lower limit = - E = 12.79 - 0.61 = 12.18

Upper limit = + E = 12.79 + 0.61 = 13.40

The 95​% confidence interval has a lower limit of $12.18 and an upper limit of $13.40

b) From above part,

The margin of error for this​ interval is ​$0.61 .