Question

Go to an online normal random variable generator; and generate 20 normally distributed random numbers. State these numbers that you generated. Construct a 95% confidence interval for the mean of these numbers. Does your confidence interval contain the initially assigned mean?

Answer 1

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:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

Mean = $\frac{-1.01}{20} = -0.0505$

Standard Deviation, $\sigma$ = $\frac{20.728095}{20} = 1.02$

Confidence interval = $\mu \pm z_{Critical}\displaystyle\frac{\sigma}{\sqrt n}$

At 95%, $z_{Critical} = 1.96$

Putting all the values, we get the confidence interval as:

$(-0.0505 \pm 0.456) = (-0.507,0.406)$