SOLUTION: If n=31, ¯ x (x-bar)=41, and s=18, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population. Give your answe

Question 1201713: If n=31,
¯
x
(x-bar)=41, and s=18, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.
Give your answers to one decimal place.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample size is 31
sample mean is 41
sample standard deviation is 18
t = (x - m) / s
s is the standard error
standard error = standard deviation / square root of sample size = 18 / sqrt(31) = 3.232895436.
critical t-score for 90% confidence interval at 30 degrees of freedom = plus or minus 1.697260851.
use criticsl t-score formula to find critical raw score.
on the low side, you get -1.697260851 = (x - 41) / 2.232895436.
solve for x to get x = -1.697260851 * 2.232895436 + 41 = 35.51293314.
on the high side, you get 1.697260851 = (x - 41) / 2.232895436.
solve for x to get x = 1.697260851 * 2.232895436 + 41 = 46.48706686.
your 90% confidence interval is from 35.5 to 46.5.

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