Find a 95% confidence interval for population mean

chwala
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Homework Statement
see attached
Relevant Equations
t distribution
I am refreshing on this...

1662157094596.png


I think there is a mistake on the circled part in red...right? not correct symbol for sample mean...This is the part that i need clarity on.

1662157179394.png


The other steps to solution are pretty easy to follow...as long as one knows the t-formula and also the knowledge to interpret the t-distribution table with dof_{1} = ##9## and significance level i.e dof_{2}= ##0.025## that gives us the desired ##2.262##.

cheers
 
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The calculation is fine. The only thing I see wrong is that they wrote x for the sample mean instead of ##\bar x##. Possibly a typo or maybe the author is unable to write this symbol.
 
Mark44 said:
The calculation is fine. The only thing I see wrong is that they wrote x for the sample mean instead of ##\bar x##. Possibly a typo or maybe the author is unable to write this symbol.
@Mark44 This is from a Further Maths Examination Paper Mark scheme.
 
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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