SOLUTION: n = 96, x = 79.7, 􏰀 = 6.0; 99% confidence

Question 1201598: n = 96, x = 79.7, 􏰀 = 6.0; 99% confidence
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
not sure what you are looking for, but i would guess you are looking for the 99% confidence interval, using either the t-score or the z-score.
what i get is:
sample size is 96.
either sample mean 79.7.
either sample standard deviation or population standard deviation is 6.
if you are dealing with the population standard deviation, then use of the z-score is implied.
if you are dealing with the sample standard deviation, then use of the t-score would be implied.
because the sample size is large, there shouldn't be a large difference between them.
since you are looking for the mean of a sample of specified size, the standard error is used rather than the standard deviation.
standard error = standard deviation / square root of sample size = 6 / sqrt(96) = .6123724357.

99% confidence interval using the z-score gets you critical z = plus or minus 2.575829303.
use the z-score formula to get the raw score.
on the high side, z = (x - m) / s becomes 2.575829303 = (x - 79.7) / .6123724357.
solve for x to get x = 2.575829303 * .6123724357 + 79.7 = 81.27736686.
on the low side, z = (x - m) / s becomes -2.575829303 = (x - 79.7) / .6123724357.
solve for x to get x = -2.575829303 * .6123724357 + 79.7 = 78.12263314.
your 99% confidence interval using the z-score is from 78.12263314 to 81.27736686. *****

99% confidence interval using the t-score gets you critical t with 95 degrees of freedom = plus or minus 2.628575664.
use the t-score formula to get the raw score.
on the high side, t = (x - m) / s becomes 2.628575664 = (x - 79.7) / .6123724357.
solve for x to get x = 2.628575664 * .6123724357 + 79.7 = 81.30966728.
on the low side, t = (x - m) / s becomes -2.628575664 = (x - 79.7) / .6123724357.
solve for x to get x = -2.628575664 * .6123724357 + 79.7 = 78.09033272.
your 99% confidence interval using the t-score is from 78.09033272 to 81.30966728. *****

as you can see, the differnce becween z-score confidence interval and t-score confidence interval is not large.
this is because the sample size is large.
if the sample size was smaller (less than 20 or so), the difference would be more pronounced.

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