The American Shark and Fat Cats inc. bank investigates the internal costs of their services, and in particular of the checking accounts that they offer. A random sample of 600 checking accounts has produced a mean annual cost of $ 500. (a) Assume that the standard deviation of annual costs of all such checking ac- counts is $40. Compute a 99% confidence interval for the current mean annual cost of the Shark and Fat Cats inc. checking accounts. (b) Assume that the standard deviation of annual costs of all such checking ac- counts is not known but that the costs are normally distributed. Compute a 99% confidence interval for the current mean annual cost of all such checking accounts, given that an unbiased sample variance estimator of 1600 ($ squared) was obtained from the sample. (c) In the situation above, assuming known standard deviation of $ 40 again, the bank has decided before sampling to change their checking account offer in case that there is evidence that the annual cost in the whole population is is on average higher than $ 450. Is there such evidence from a sample mean of $ 500? How strong is it?
The American Shark and Fat Cats inc. bank investigates the internal costs of their services, and in particular of the checking accounts that they offer. A random sample of 600 checking accounts has produced a mean annual cost of $ 500. (a) Assume that the standard deviation of annual costs of all such checking ac- counts is $40. Compute a 99% confidence interval for the current mean annual cost of the Shark and Fat Cats inc. checking accounts. (b) Assume that the standard deviation of annual costs of all such checking ac- counts is not known but that the costs are normally distributed. Compute a 99% confidence interval for the current mean annual cost of all such checking accounts, given that an unbiased sample variance estimator of 1600 ($ squared) was obtained from the sample. (c) In the situation above, assuming known standard deviation of $ 40 again, the bank has decided before sampling to change their checking account offer in case that there is evidence that the annual cost in the whole population is is on average higher than $ 450. Is there such evidence from a sample mean of $ 500? How strong is it?
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Author:Amos Gilat
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Transcribed Image Text:The American Shark and Fat Cats inc. bank investigates the internal costs of their
services, and in particular of the checking accounts that they offer. A random sample
of 600 checking accounts has produced a mean annual cost of $ 500.
(a) Assume that the standard deviation of annual costs of all such checking ac-
counts is $40. Compute a 99% confidence interval for the current mean annual
cost of the Shark and Fat Cats inc. checking accounts.
(b) Assume that the standard deviation of annual costs of all such checking ac-
counts is not known but that the costs are normally distributed. Compute a
99% confidence interval for the current mean annual cost of all such checking
accounts, given that an unbiased sample variance estimator of 1600 ($ squared)
was obtained from the sample.
(c) In the situation above, assuming known standard deviation of $40 again, the
bank has decided before sampling to change their checking account offer in
case that there is evidence that the annual cost in the whole population is is
on average higher than $450. Is there such evidence from a sample mean of $
500? How strong is it?
(d) The statisticians at the bank have computed a confidence interval based on the
assumption that the standard deviation of annual costs of all such checking
accounts is 40 dollars. A member of the board of directors has questioned this
assumption. Another random sample of checking accounts from this population
is taken and the observed costs are in $
400, 420, 340, 460, 380, 410, 850, 450, 440, 510.
Compute a 99% CI for the standard deviation. What do you think about the
initial assumption that the true standard deviation is 40$?
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