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AP Statistics: Section 12.1 B Example: A bank wonders if omitting the annual credit card fee for customers who charge at least $2400 a year would increase the amount that customers charge on its credit cards. The bank makes this offer to a SRS of 200 of its credit card customers. It then compares the amount these customers charged this year to the amount they charged last year. The mean increase is $332 and the standard deviation is $108. a) Is there significant evidence at the 1% level that the mean amount charged increases under the nofee offer? Hypothesis: The population of interest is credit card customers at this bank. H0 : 0 H a : 0 where the mean difference in the amount of money charged on credit cards with the 2 policies. Conditions: SRS : Yes Normality of x : n 200 means the CLT will give x a distribution that is approx. Normal Independence : No reason not to assume observations are independent and since sampling w/o replacement N 10n Calculations: t 332 0 43.474 108 200 Interpretation: Since my p - value is less than the significance level of .01, I reject the H 0 . I conclude that the amount charged on credit cards by this bank' s customers increases under the no - fee plan. b) Construct and interpret a 99% confidence interval for the mean amount of the increase omitting the annual credit card fee for customers who charge at least $2400 a year would increase the amount that customers charge on its credit cards. x t s 108 332 2.626 n 200 311.946,352.054 I am 99% confident that the mean increase in the amount charged to credit cards under the banks no - fee program is between 311.946 and 352.054 dollars. c) Does our work in parts a & b show that omitting the annual credit card fee for customers who charge at least $2400 a year caused an increase the amount that customers charge on its credit cards? NO. there could be confounding variables such as an improvement in the economy that caused the increase. d) Briefly describe the design of an experiment to study the no-fee offer. Choose a second SRS of 200 customers to use as a control group. Compare the mean increase of the two groups. The t procedures are robust against non-Normality of outliers or the population except when _________ _________________ strong skewness are present. (Skewness is more serious than other kinds of non-Normality). Review the guidelines in the box “Using the t-procedures” on page 655. As the sample size increases, the ______ CLT ensures that the distribution of the sample mean becomes more nearly Normal and the t-distribution becomes more accurate for calculating p-values. The power of a statistical test measures its ability to detect deviations from the ____. H 0 The power of the one-sample t -test against a specific alternative value of the population mean is the probability that the test will _____________ reject the H 0 when the mean has the alternative value.