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 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?

Answer 1

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

b) $0.57

Explanation:

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

`\alpha = (1-0.95)/(2) = 0.025`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.025 = 0.975`, so
`z = 1.96`

Now, find the margin of error M as such

`M = z*(\sigma)/(√(n))`

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

`M = 1.96*(1.86)/(√(41)) = 0.57`

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