Sta 220 Statistics Mr Smith Room 310 Class

Sta 220 - Statistics Mr. Smith Room 310 Class #16

Section 5 -1 and 5 -2 Notes

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.

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

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

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.

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

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

Example 5. 1: •

Solution •

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

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

Example 5 -2: •

Solution •

Table 7. 2 Copyright © 2013 Pearson Education, Inc. . All rights reserved.

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

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

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.

Solution •

Example 5 -4 •

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

Solution •

(10. 084, 16. 316) 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 10. 084 and 16. 316 minutes.

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

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