Find a 95% confidence interval for population mean

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The discussion centers on identifying a potential error in the notation used for the sample mean in a statistical problem. Participants agree that the calculation for the 95% confidence interval is correct, but the symbol used for the sample mean should be ##\bar x## instead of just x. The clarity of the t-distribution table interpretation and the use of the t-formula are acknowledged as straightforward for those familiar with the concepts. The issue appears to be a simple typographical error in the examination paper. Overall, the focus remains on ensuring accurate representation of statistical symbols in educational materials.
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.
 

Thread 'Does this series converge uniformly?'

First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...
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