Answer: 20 ± 11.32
Explanation: Confidence Interval (CI) is an interval of values where there is a % certainty the true mean value lies in. For example, a 95% CI means there is a 95% certainty the true mean value lies in the interval.
For the data set 2, z-value for 95% confidence interval is z = 1.96
Formula to calculate CI is
x ± [tex]z\frac{s}{\sqrt{n} }[/tex]
where
x is mean
z is z-value
s is standard deviation
n is the sample number
Then:
20 ± [tex]1.96\frac{10}{\sqrt{3} }[/tex]
20 ± [tex]1.96\frac{10}{1.7320}[/tex]
20 ± [tex]\frac{19.6}{1.7320}[/tex]
20 ± 11.32
The 95% CI is 20 ± 11.32, which means there is a 95% certainty the true value is between 8.68 and 31.32.
