Why Divide by n 1? Let a population consist of the values

Chapter 3, Problem 45

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Why Divide by n 1? Let a population consist of the values 2 min, 3 min, 8 min.(These are departure delay times taken from American Airlines flights from New Yorks JFKairport to Los Angeles. See Data Set 15 in Appendix B.) Assume that samples of two valuesare randomly selected with replacement from this population. (That is, a selected value is replacedbefore the second selection is made.)a. Find the variance s2 of the population {2 min, 3 min, 8 min}.b. After listing the nine different possible samples of two values selected with replacement,find the sample variance s2 (which includes division by n - 1) for each of them; then findthe mean of the nine sample variances s2. c. For each of the nine different possible samples of two values selected with replacement, findthe variance by treating each sample as if it is a population (using the formula for populationvariance, which includes division by n), then find the mean of those nine population variances.d. Which approach results in values that are better estimates of s2: part (b) or part (c)? Why?When computing variances of samples, should you use division by n or n - 1?e. The preceding parts show that s2 is an unbiased estimator of s2. Is s an unbiased estimatorof s? Explain