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Question 487:



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For a sample this small, we'll need to use the critical value from the t-distribution. We can find this by using Excel or a t-table. In excel, we'd use the formula =TINV(.10, 15) where the parameters are the 1- the confidence level and the degrees of freedom or 1 less than the sample size. This gets us the critical value for a 90% confidence interval of 1.75.  We'll use this shortly.

Next we need to find the standard error of the mean (SEM) which is made up of the standard deviation divided by the square root of the sample size. We're given the standard deviation of 27 and sample size of 16 making the SEM = 27/SQTY(16) = 27/4 = 6.75. 

We now find the margin of error by multiplying the SEM times the critical value of 1.75 we found earlier. The margin or error would be 6.75*1.75 = 11.81.

The confidence interval is generated by adding and subtracting this value from the mean. So 127-11.81 and 127+11.81  = 115.19 and 138.81.

The 90% Confidence interval is between 115.19 and 138.81.

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