Please Help Stats Confidence Level

This my first posting.

The Bank wants to estimate the mean dollars that each card holder will spend each month. It would like to be within plus or minus $10 of the true mean with a 98% confidence level. The standard deviation is thought to be $500. How many card holders should be sampled? After you?ve determined how many card holders should be sampled, The Bank comes back and says that it will cost $5 per sample and they were only planning on spending $10,000 on the sample. In a memo to the Bank product development team indicate how many card holders should be sampled to meet the original requirements of the sample. Then explain the trade-offs that will occur when you lower the sample to $10,000 to meet their budget. This is what I came up with is this anywhere near right.

n= (Z a/2 x $500 ) = 2000 = (2.33 x $500) = 116.50 /10sq = 3.16=.99 or 99% $10 $10


So I did n=13,573 x $5 = 67,865 / 2 = 33932.5

z a/2 = 2.33 t

2.33 x 33933= 79062.73 / 10 sq= 3.16 = .99 or 99%

.99 came from the table when i matched -3.0 + .16


TS Contributor
You're on the right track - it just appears to be some computational errors.

The formula for minimum sample size is:

n = ((Zc * s)/d)^2

where Zc = z score (for 98% confidence, 2-tailed = 2.326)
s = standard deviation = 500
d = margin of error = 10

I got a sample size of n = 13,526 and when multiplied by $5 each, that's $67,630.

Now, force n = 2000, since at $5 per sample, they can only afford $10,000

With n = 2000, figure out what d would be if everything else is held the same, then figure out what Zc would be (and hence the confidence level) if everything else is the same.

:D John,

Thank you so much, this was the first time I use this system. So, I was a little weiry about accessing for help. I did continue to work on the assignment and got a B+. He said he only gave me this grade because I was unable to give more specific details. I just now looked back at your response and thank you. I will continue to check in periodically because you were helpful in letting me know I was on the right track.