Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 10. Listed below are the nine different samples. Complete parts (a) through (d).
1,1 1,4, 1,10 4,1 4,4 4,10 10,1 10,4 10,10
(a) Find the value of the population variance σ²
(b) Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution.
(c) Find the mean of the sampling distribution of the sample variance.
(d) Based on the preceding results, is the sample variance an unbiased estimator of the population variance? Why or why not?
