Question 1162723: Determine the minimum sample size required when you want to be 90% confident that the sample mean is within one unit of the population mean and standard deviation is 2.1. Assume the population is normally distributed.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Use a z-iinteval.
half-interval is z*sigma/sqrt(n), where z=1.645 for 90% interval
1.645*2.1/sqrt(n)=1
n=11.93 or 12. (interval is 9.00, 10.997)
This is assuming the population is normally distributed with sigma=2.1
NOTE:
It wasn't stated here, but if the sample sd was 2.1 and not the population sd, then one needs a t-interval.
The t-interval will require a slightly larger sample size since the t-value for n=12 is about 8-9% greater than the z-value. Squaring that will make a sample size about 1.18 times larger, and n should be at least 14 or maybe 15. Check both of those numbers
with n=15, the interval is (9.05, 10.95) within 1 unit of 10 (pick any mean)
with n=14, the interval is (9.006, 10.994) still 1 unit away.
minimum sample size is 14.
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