Question

Samples of size n = 20 are randomly selected from 4 different bins of DVDs ranging in price from $4.99 to $9.99. You return each DVD before randomly drawing another and calculate the variance of each sample. What is the distribution of the sample variance?

Answer 1

We are given that, DVDs ranging in price from $4.99 to $9.99.

Therefore,

Range = Highest value - Lowest value = 9.99 - 4.99 = 5.

From this known value of Range, now we can find Standard deviation.

The range rule of thumb says that the

Standard deviation S = Range / 4.

Standard deviation S = 5 / 4 = 1.25.

Variance S^2 = 1.25^2 = 1.5625.

Now let us calculate the variance of each sample,

Sample Size = n = 20

standard deviation S = 1.25.

Standard deviation of the Sample = S / √n = 1.25 / √20 = 0.27951.

Variance of the Sample = 0.27951^2 = 0.078125.

What is the distribution of the sample variance?

The Sample variance S^2 follows Chi square distribution with degrees of freedom = n-1 = 20-1 = 19.

Chi square distribution is skewed to the right.