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I'm working through the questions in this book. One question asks to construct a 90% confidence interval when the variable has a mean of 11 and a standard deviation of 1.8, and n = 4.

Here's my workings out:

sd/sqrt(n) = 1.8/sqrt(4) = 1.8/2 = 0.9

Upper = 11 + 1.645 x 0.9 = 12.48

Lower = 11 + 1.645 x 0.9 = 9.52

So my 90% confidence interval is 9.5-12.5.

But the book says the 90% confidence interval is 8.9-13.1.

Where am I going wrong?

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As the sample size is small, the confidence interval determination should be based on a t-distribution. That way you can get the answer given in the book.

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