[Statistics] measuring values against known value

Chickenpoxpie
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Homework Statement


You use a standard gram weight of known weight (x) to check the accuracy of a balance. For one balance, this standard is weighed 3 times yielding the following values; a, b, and c. Calculate the 95% confidence limit for the mean


Homework Equations


general statistics and mean equations
ts/n^1/2

The Attempt at a Solution


I am confused how to do this problem because of the known value. At first I did the problem ignoring the known value and going through all the motions (figuring the mean, standard dev, and then plugging into ts/n^1/2 for 2 degrees of freedom) but how do things change because of the known weight and "testing for the accuracy of the balance"?
 
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Nevermind y'all, was a silly mistake. I can easily do a one sample t test
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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