# Consider the following data set below. Find the UPPER INTERVAL of the population mean at 80\% confidence interval. Given: 12,10,9,11

Consider the following data set below. Find the UPPER INTERVAL of the population mean at $80\mathrm{%}$ confidence interval. (write your answer in two decimal places) Given: 12,10,9,11
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It is given that,
12,10,9,11
Thus,
Sample mean, $\stackrel{―}{x}=\frac{\sum _{t-1}^{n}{X}_{t}}{n}=10.5$
Sample standard deviation, $s=\sqrt{\frac{\sum _{t-1}^{n}{\left({X}_{t}-\stackrel{―}{X}\right)}^{2}}{n-1}}=1.29099$
Since, Population standard deviation is unknown thus t distribution is used.
Sample size, $n=4$
Degree of freedom $=n-1=4-1=3$
The value of ${t}_{\frac{\alpha }{2},n-1}$ at $80\mathrm{%}$ confidence interval is $=1.638$ [From t table]
Step 2
Now, the $80\mathrm{%}$ confidence interval for the population mean can be calculated as:
$CI=\stackrel{―}{x}±{t}_{\frac{\alpha }{2},n-1}×\frac{s}{\sqrt{n}}$
$=10.5±1.638×\frac{1.29099}{\sqrt{4}}$
$=\left(9.44,11.56\right)$
Upper limit $=11.56$