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In: Statistics and Probability

Banking fees have received much attention during the recent economic recession as banks look for ways...

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 ​$11.95 per month on their​ interest-bearing checking accounts. Assume the population standard deviation is ​$1.67. 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 ​. ​(Round to the nearest cent as​ needed.)

b. What is the margin of error for this​ interval

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Expert Solution

ANSWER:

Given that,

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 ​$11.95 per month on their​ interest-bearing checking accounts. Assume the population standard deviation is ​$1.67. Complete parts a and b below.

Sample size = n = 41

Mean = = 11.95

Population standard deviation = = 1.67

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 ​. ​(Round to the nearest cent as​ needed.)

c = 99% =99/100 =0.99

= 1-c = 1-0.99 = 0.01

/2 = 0.01/2 = 0.005

Critical value = Z/2 = Z0.005 = 2.58

99% CI = Z/2 * (/sqrt(n))

99% CI = 11.95 2.58 * (1.67/sqrt(41))

99% CI = 11.95 0.67289027

99% CI = 11.95 - 0.67289027 , 11.95 +0.67289027

99% CI = 11.27710973 , 12.62289027

99% CI = 11.28 to 12.62

b. What is the margin of error for this​ interval

Margin of error = Z/2 * (/sqrt(n))

Margin of error =2.58 * (1.67/sqrt(41))

Margin of error = 0.67289027

Margin of error = 0.67289

----------------------------------------------------------------------The End ------------------------------------------------------------------------

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