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 34 customers paid an average fee of

$12.47per month on their interest-bearing checking accounts. Assume the population standard deviation is $1.51

Complete parts a and b below.

a. Construct a 99% confidence interval to estimate the average fee for the population. The 99 % confidence interval has a lower limit of

$ ? and an upper limit of $ ?.

b. What is the margin error for this interval?

Answer 1

As here population standard deviation is known so we will use z distribution to find CI

z value for 99% CI is 1.96 as P(-2.58<z<2.58)=0.99

(a)

= [12.47- 2.58*1.51/34 , 12.47+ 2.58*1.51/34]

= [12.47- 0.6681, 12.47+ 0.6681]

= [11.8019, 13.1381]

Lower limit is 11.8019

Upper Limit is 13.1381

(b)

Margin of error = {(z.σ)/√n}

= (2.58*1.51)/34

= 0.6681

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