Answer:
(-0.507,0.406)
Step-by-step explanation:
The online normal variable generator gave the following data set with n = 20
-0.42,-0.74,-1.54,1.16,1.19,0.32,-0.63,0.95,-1.8,1.49,0.02,0.7,0.56,-1.28,0.16,-0.05,0.28,-0.82,1.25,-1.81
For a normally distributed data,
Mean = 0 and Standard deviation = 1
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/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]
Mean = [tex]\frac{-1.01}{20} = -0.0505[/tex]
Standard Deviation, [tex]\sigma[/tex] = [tex]\frac{20.728095}{20} = 1.02[/tex]
Confidence interval = [tex]\mu \pm z_{Critical}\displaystyle\frac{\sigma}{\sqrt n}[/tex]
At 95%, [tex]z_{Critical} = 1.96[/tex]
Putting all the values, we get the confidence interval as:
[tex](-0.0505 \pm 0.456) = (-0.507,0.406)[/tex]
