Banking fees have received much attention during the recent economic recession as banks look for ways to recover from the crisis. A sample of 41 customers paid an average fee of $12.22 per month on their interest-bearing checking accounts. Assume the population standard deviation is $1.86. Complete parts a and b below. a. Construct a 95% confidence interval to estimate the average fee for the population.
b. What is the margin of error for this interval?

a) The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79

b) $0.57

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

So the answer for b) is $0.57.

The lower end of the interval is the sample mean subtracted by M. So it is 12.22 - 0.57 = $11.65

The upper end of the interval is the sample mean added to M. So it is 12.22 + 0.57 = $12.79

The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79

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