Answer:
95% Confidence interval: (6.34,14.66)
Step-by-step explanation:
We are given the following data set:
5, 20, 18, 3, 10, 2, 6, 9, 19, 13
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{105}{10} = 10.5[/tex]
Sum of squares of differences =
30.25 + 90.25 + 56.25 + 56.25 + 0.25 + 72.25 + 20.25 + 2.25 + 72.25 + 6.25 = 406.5
[tex]S.D = \sqrt{\frac{406.5}{9}} = 6.72[/tex]
Confidence interval:
[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
[tex]10.5 \pm 1.96(\dfrac{6.72}{\sqrt{10}} ) = 10.5 \pm 4.16 = (6.34,14.66)[/tex]
