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5 June, 16:04

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?

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  1. 5 June, 16:22
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    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.
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