Essentials of Statistics, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780321926739
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 3.3, Problem 45BB
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 York’s JFK airport to Los Angeles. See Data Set 15 in Appendix B.) Assume that samples of two values are randomly selected with replacement from this population. (That is, a selected value is replaced before the second selection is made.)
- a. Find the variance σ2 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 find the
mean of the nine sample variances s2. - c. For each of the nine different possible samples of two values selected with replacement, find the variance by treating each sample as if it is a population (using the formula for population variance, 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 σ2: 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 σ2. Is s an unbiased estimator of σ? Explain.
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Chapter 3 Solutions
Essentials of Statistics, Books a la Carte Edition (5th Edition)
Ch. 3.2 - Employment Data listed below are results from the...Ch. 3.2 - Average The web site IncomeTaxList.com lists the...Ch. 3.2 - Median In an editorial, the Poughkeepsie Journal...Ch. 3.2 - Prob. 4BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 8BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 10BSC
Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 14BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 18BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - Prob. 23BSCCh. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - Large Data Sots from Appendix B. In Exercises...Ch. 3.2 - Prob. 26BSCCh. 3.2 - Prob. 27BSCCh. 3.2 - Prob. 28BSCCh. 3.2 - Prob. 29BSCCh. 3.2 - In Exercises 29-32, find the mean of the data...Ch. 3.2 - Prob. 31BSCCh. 3.2 - In Exercises 29-32, find the mean of the data...Ch. 3.2 - Degrees of Freedom Carbon monoxide is measured in...Ch. 3.2 - Prob. 34BBCh. 3.2 - Trimmed Mean Because the mean is very sensitive to...Ch. 3.2 - Prob. 36BBCh. 3.2 - Prob. 37BBCh. 3.2 - Quadratic Mean The quadratic mean (or root mean...Ch. 3.2 - Prob. 39BBCh. 3.3 - Comparing Variation Which do you think has less...Ch. 3.3 - Correct Statements? Which of the following...Ch. 3.3 - Variation and Variance In statistics, how do the...Ch. 3.3 - Prob. 4BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 7BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 9BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 11BSCCh. 3.3 - Prob. 12BSCCh. 3.3 - Prob. 13BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 15BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 18BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 21BSCCh. 3.3 - Prob. 22BSCCh. 3.3 - Prob. 23BSCCh. 3.3 - Prob. 24BSCCh. 3.3 - Prob. 25BSCCh. 3.3 - Prob. 26BSCCh. 3.3 - Prob. 27BSCCh. 3.3 - Prob. 28BSCCh. 3.3 - Prob. 29BSCCh. 3.3 - Estimating Standard Deviation with the Range Rule...Ch. 3.3 - Prob. 31BSCCh. 3.3 - Prob. 32BSCCh. 3.3 - Prob. 33BSCCh. 3.3 - Prob. 34BSCCh. 3.3 - Identifying Unusual Values with the Range Rule of...Ch. 3.3 - Prob. 36BSCCh. 3.3 - Prob. 37BSCCh. 3.3 - Finding Standard Deviation from a Frequency...Ch. 3.3 - Prob. 39BSCCh. 3.3 - Finding Standard Deviation from a Frequency...Ch. 3.3 - Prob. 41BSCCh. 3.3 - The Empirical Rule Based on Data Set 3 Body...Ch. 3.3 - Prob. 43BSCCh. 3.3 - Chebyshev's Theorem Based on Data Set 3 in...Ch. 3.3 - Why Divide by n 1? Let a population consist of...Ch. 3.3 - Prob. 46BBCh. 3.4 - z Scores James Madison, the fourth President of...Ch. 3.4 - Prob. 2BSCCh. 3.4 - Prob. 3BSCCh. 3.4 - Prob. 4BSCCh. 3.4 - Prob. 5BSCCh. 3.4 - Prob. 6BSCCh. 3.4 - Prob. 7BSCCh. 3.4 - Prob. 8BSCCh. 3.4 - Prob. 9BSCCh. 3.4 - Prob. 10BSCCh. 3.4 - Usual and Unusual Values.In Exercises 9-12,...Ch. 3.4 - Usual and Unusual Values.In Exercises 9-12,...Ch. 3.4 - Prob. 13BSCCh. 3.4 - Prob. 14BSCCh. 3.4 - Comparing Values.In Exercises 13-16, use z scores...Ch. 3.4 - Prob. 16BSCCh. 3.4 - Percentiles. In Exercises 17-20, use the following...Ch. 3.4 - Prob. 18BSCCh. 3.4 - Prob. 19BSCCh. 3.4 - Prob. 20BSCCh. 3.4 - Prob. 21BSCCh. 3.4 - Prob. 22BSCCh. 3.4 - Prob. 23BSCCh. 3.4 - Prob. 24BSCCh. 3.4 - Prob. 25BSCCh. 3.4 - Prob. 26BSCCh. 3.4 - Prob. 27BSCCh. 3.4 - Prob. 28BSCCh. 3.4 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.4 - Prob. 30BSCCh. 3.4 - Prob. 31BSCCh. 3.4 - Boxplots. 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