Question 1041239
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Add up the values to get 49111. 
Then divide that sum by 12 to get the sample mean to be 4092.58333333333. 
So xbar = 4092.58333333333


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Use a calculator to compute the standard deviation to be 611.079292330506. 
Doing the standard deviation by hand would take a very long time. 
So s = 611.079292330506


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The degrees of freedom is df = n-1 = 12-1 = 11


Use this <a href = "http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">table</a> to highlight the "90% confidence level" column and the row that has df = 11. The value at this row and column combo is 1.796. This is the t-critical value

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Summary
sample mean = xbar = 4092.58333333333
t critical value = t = 1.796
standard deviation = s = 611.079292330506
sample size = n = 12


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We'll use those values in the summary (above) to compute the lower and upper boundaries of the confidence interval


Lower boundary L
L = xbar - t*s/sqrt(n)
L = 4092.58333333333 - 1.796*611.079292330506/sqrt(12)
L = 3775.76283239028
L = 3775.763 ... rounding to three decimal places


Upper boundary U
U = xbar + t*s/sqrt(n)
U = 4092.58333333333 + 1.796*611.079292330506/sqrt(12)
U = 4409.40383427639
U = 4409.404 ... rounding to three decimal places


So the confidence interval, accurate to three decimal places, is <font color=red>3775.763</font> < mean < <font color=red>4409.404</font>


If your book requires different decimal precision, then be sure to round in a different way. 
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