Please Help Stats Confidence Level

#1
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

or

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
 

JohnM

TS Contributor
#2
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.
 
#3
Thankyou

: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.

Thankful
AJ