A bank wonders whether omitting the annual credit card fee for customers who charge at least $2400 in a year would increase the amount charged on its credit card. The bank makes this offer to an SRS of 250 of its existing credit card customers. It then compares how much these customers charge this year with the amount that they charged last year. The mean increase is $342, and the standard deviation is $108.

(a) Is there significant evidence at the 1% level that the mean amount charged increases under the no-fee offer? State Math Notationand Math Notation and carry out a t-test.

(b) Give a 95% confidence interval for the mean amount of the increase.

(c) The distribution of the amount charged is skewed to the right, but outliers are prevented by the credit limit that the bank enforces on each card. Use of the t procedures is justified in this case even though the population distribution is not normal. Explain why.

Question

Giada Molina

Mathematics

7 September, 18:59

A bank wonders whether omitting the annual credit card fee for customers who charge at least $2400 in a year would increase the amount charged on its credit card. The bank makes this offer to an SRS of 250 of its existing credit card customers. It then compares how much these customers charge this year with the amount that they charged last year. The mean increase is $342, and the standard deviation is $108.

(a) Is there significant evidence at the 1% level that the mean amount charged increases under the no-fee offer? State Math Notationand Math Notation and carry out a t-test.

(b) Give a 95% confidence interval for the mean amount of the increase.

(c) The distribution of the amount charged is skewed to the right, but outliers are prevented by the credit limit that the bank enforces on each card. Use of the t procedures is justified in this case even though the population distribution is not normal. Explain why.

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Answers (2)

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Alissa Li · Answer 1

Hello there.

(

b) Give a 95% confidence interval for the mean amount of the increase.

(b) The confidence interval is 308 < x < 376

Karina Stanley · Answer 2

(a) At a 1% level of significance, there shows to be an increase in the mean amount charged under the no-fee offer.

(b) The confidence interval is 308 < x < 376

(c) The t test is justified since the data can be still be viewed as a normally distributed by viewing the graph as a gamma distribution.