A bank wonders whether omitting the annual credit card fee for customers who charge at leats...

A bank wonders whether omitting the annual credit card fee for customers who charge at leats $2500 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of 200 of its credit card customers. It then compares how much these customers charge this year with the amount that they charged last year. The mean increase in the sample is $346, and the standard deviation is $112. Give a 99% confidence interval for the mean amount charges would have incremented if this benefit had been extended to all such customers.
Z* for 99% confidence is 2.58.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 346

Population standard deviation = = 112

Sample size = n = 200

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.58

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

= 2.58 * (112 / $\sqrt$ 200 )

= 20.43

At 99% confidence interval estimate of the population mean is,

± E

346 ± 20.43

( $ 325.57, $ 366.43 )

orchestra answered 2 years ago

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