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

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.

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

how far were you able to get?

anonymous · Answer

im kinda working backwards on this because i didn't know how to do a
for c i got 
c) the company gives a limit and the sample size is big so we can assume that extreme outliers are unlikely to appear so the CLT says x bar is normally distributed (approx.)

jim_thompson5910 · Answer

ok I see what they're asking now

yes for part c, since the sample size is very large (definitely larger than 30), you can use the normal distribution even if the population isn't necessarily normally distributed due to the central limit theorem

jim_thompson5910 · Answer

are you able to find the t test statistic?

anonymous · Answer

for which part of the question

jim_thompson5910 · Answer

part a

anonymous · Answer

wouldn't you look for the 99% confidence

jim_thompson5910 · Answer

You would use this formula

$$\LARGE t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$$

does that look familiar?

anonymous · Answer

yes give me a second to find t @jim_thompson5910

anonymous · Answer

what would u be in this situation @jim_thompson5910

anonymous · Answer

never mind i got it

anonymous · Answer

50.069396286? @jim_thompson5910

jim_thompson5910 · Answer

ok let me check

anonymous · Answer

okay

jim_thompson5910 · Answer

yeah I'm getting the same t value

anonymous · Answer

okay great! now what

jim_thompson5910 · Answer

we need to use the t-distribution

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