# Question

In Table 6.1 we considered the 15 possible samples of two observations from a population of N = 6 values of years on the job for employees. The population variance for these six values is as follows:

σ = 47 / 12

For each of the 15 possible samples, calculate the sample variance. Find the average of these 15 sample variances, thus confirming that the expected value of the sample variance is not equal to the population variance when the number of sample members is not a small proportion of the number of population members.

In fact, as you can verify here,

E[s2] = Nσ2 / (N – 1)

σ = 47 / 12

For each of the 15 possible samples, calculate the sample variance. Find the average of these 15 sample variances, thus confirming that the expected value of the sample variance is not equal to the population variance when the number of sample members is not a small proportion of the number of population members.

In fact, as you can verify here,

E[s2] = Nσ2 / (N – 1)

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