<PRE><B>Question 1202936</B>
sample mean is 22
sample standard deviation is 7
sample size is 15
population mean is assumed to be 22 plus or minus a margin of error.
90% two tailed confidience interval with 14 degrees of freedom leads to a critical t-score of plus or minus 1.7613.
at 1.7613 t-score, the t-score formula becomes 1.7613 = (x - 22) / s, where s is the standard error.
s = standard deviation of sample divided by square root of sample size = 7 / sqrt(15) = 1.80739.
when t = 1.7613, t-score formula becomes 1.7613 = (x - 22) / 1.80739.
solve for x to get x = 25.183356.
round to 4 decimal places = 25.1834.
when t = -1.7613, t-score formula becomes -1.7613 = (x - 22) / 1.80739.
solve for x to get x = 18.81664.
round to 4 decimal places = 18.8166
your 90% confidence interval indicates the true population mean will be somewhere between 18.8166 and 25.1834.
the margin of error is equal to the mean plus or minus (25.1834 - 22) = 3.1834
22 + 3.1834 = 25.1834
22 - 3.1834 = 18.8166
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