Respuesta :
Answer:
98% Confidence Interval: (2.387,9.113 )
Step-by-step explanation:
We are given the following data set:
3, 8, 3, 5, 1, 13, 9, 2, 7, 3, 13, 2
a) 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{69}{12} = 5.75[/tex]
Sum of squares of differences = 196.25
[tex]S.D = \sqrt{\frac{196.25}{11}} = 4.044[/tex]
b) 98% Confidence Interval:
[tex]\bar{x} \pm z_{critical}\displaystyle\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.02} = \pm 2.33[/tex]
[tex]5.75 \pm 2.33(\displaystyle\frac{5}{\sqrt{12}} ) = 5.75 \pm 3.363 = (2.387,9.113 )[/tex]
