1. The Practice of Statistics Third Edition Chapter 9: Sampling Distributions Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates

2. The distribution of returns for NYSE common (individual) stocks in 1987 Note wide spread; mean return is -3.5 The distribution of returns for portfolios of 5 stocks in 1987 Note smaller spread; mean return is still -3.5

3. Important points from the histograms -Means of random samples are less variable than individual observations. -Means of random samples are more Normal than individual observations.

5. Important points about the behavior of sample means in repeated samples: -The sample mean xbar is an unbiased estimator of the population mean μ -Variability of the distribution decreases as n increases -Must meet rule of thumb one to use standard deviation formula

6. Note: These statements are true regardless of the sample size (assuming N ≥ 10n) does not approach μ it equals μ does not approach it equals

7. Height of Young Women For n = 1 ~ N(64.5, 2.5) For n = 10 ~ N(64.5, 0.79) (ignore blue for now)

8. Height of Young Women For n = 1 ~ N(64.5, 2.5) For n = 10 ~ N(64.5, 0.79) P(X > 66.5) = ? P(xbar > 66.5)= ?

9. Repeated Measurements Common practice to repeat a careful measurement several times and report the average. Think of the results of n repeated measurements as an SRS from the population of outcomes we would get if we repeated the measurement forever. The average of n results (the sample mean xbar) is less variable than a single measurement.

11. CLT If n is not large, the shape of the sampling distribution of xbar more closely resembles the shape of the original population. If population is Normal, shape of sampling distribution will be Normal regardless of sample size. If n is large, the shape of sampling distribution will be Normal regardless of population shape.

12. www.whfreeman.com/tps3e n = 1 n = 2 n = 3 n = 4

13. Servicing Air Conditioners Time required to perform preventive maintenance has an exponential distn with μ = 1 hour and σ = 1 hour. Your company has a contract to maintain 70 units. Should you a lot an average of 1.1 hours to service each unit? Or an average of 1.25 hours? CLT says that the time xbar spent working on 70 units is approximately Normally distributed with mean μ = 1 and σ = 0.120.

14. What is the P(xbar > 1.1)? What is the P(xbar > 1.25)?

15. Sampling distribution of a sample mean xbar