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Sta220 - Statistics Mr. Smith Room 310 Class #16.

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1 Sta220 - Statistics Mr. Smith Room 310 Class #16

2 Section 5-1 and 5-2 Notes

3 Our goal in this chapter is to estimate the value of an unknown population parameter, such as the population mean. Example The mean gas mileage for a new car model The average expected life of a flat-screen computer monitor.

4 The unknown population parameter (e.g., mean or proportion) that we are interested in estimating is called the target parameter.

5 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

6 A point estimator of a population parameter is a rule or formula that tells us how to use the sample data to calculate a single number that can be used as an estimate of the target parameter. An interval estimator (or confidence interval) is a formula that tells us how to use the sample data to calculate an interval that estimates the target parameter.

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8 5-2: Confidence Interval for a Population Mean: Normal (z) Statistic

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11 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Sampling distribution of

12 Example 5.1:

13 Solution

14

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16 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Confidence intervals for  : 10 samples

17 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Locating z  /2 on the standard normal curve

18

19 Example 5-2:

20 Solution

21 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 7.2

22 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

23 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

24 Example 5-3 Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected, and the number of unoccupied seats is noted for each of the sampled flights. Descriptive statistics for the data are displayed in the MINITAB printout below. Estimate μ, the mean number of unoccupied seats per flight during the past year, using 90% confidence interval.

25 Solution

26

27 Example 5-4

28 a.Calculate a 90% confidence interval for the target parameter. Interpret the results. b.Explain what the phrase “90% confidence” implies in part a.

29 Solution

30 (10.084, ) We are 90% confident that the true average amount of time per day laptops are used for taking notes for all middle school students across the country is between and minutes.

31 b. “90% confidence” means that in a repeated sampling, 90% of all confidence intervals constructed in this manner will contain the true mean.

32

33 5-2 Homework Due Friday (also 5-3 and 5-5 will be due Friday, so I encourage you to work tomorrow).


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