155S7.3.notebook
March 22, 2010
MAT 155­DY1 & DY2
Chapter 7 Estimates and Sample Size
7.3 Estimating a Population Mean: Sigma Known
Look in the Course Documents of CourseCompass for CHAPTER 7 Estimates, Sample Sizes, and Confidence Intervals
Session 4 of MAT 155 Statistical Analysis
Oct 20­7:16 AM
Mar 22­12:05 PM
1
155S7.3.notebook
March 22, 2010
Technology available for this section
Get a printable copy of the chapter notes in from Dr. Moore in the Course Documents section in CourseCompass.
S4D.1 MAT 155 Chapter 7 Estimates and Sample Sizes
155Chapter7 ( Package file )
These notes cover the following topics: point estimate; level of confidence; confidence interval for the population proportion; confidence interval for the population mean when the population standard deviation is known; confidence interval for the population mean when the population standard deviation is unknown; determine the sample size for attribute and variable sampling.
Animations and Videos in the Multimedia Library of Course Compass provide very valuable information and examples.
TI­83/84 Tutorials at http://cfcc.edu/faculty/cmoore/TI­STAT.htm
Oct 20­7:16 AM
TI­83/84 Tutorials ­ http://cfcc.edu/faculty/cmoore/TI­STAT.htm
Oct 20­7:16 AM
2
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
357/5. Find the critical value z for 95% confidence level.
Oct 20­7:16 AM
Section 7.3 Estimating a Population Mean
357/8. Find the critical value z for 99% confidence level.
Oct 20­7:16 AM
3
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
358/10. Calculate the margin of error E for 95% confidence level, n = 9, and sigma is not known.
Oct 20­7:16 AM
Section 7.3 Estimating a Population Mean
358/12. Calculate the margin of error E for 99% confidence level, n = 12, and sigma is known, and normal distribution.
NOTE: Since the population standard deviation, sigma is not known, we can not use the methods of this section.
Oct 20­7:16 AM
4
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
358/14. Construct 95% confidence interval to estimate population mean: n = 90, x­bar = 66.2, sigma = 3.4.
Oct 20­7:16 AM
Section 7.3 Estimating a Population Mean
358/14. Construct 95% confidence interval to estimate population mean: n = 90, x­bar = 66.2, sigma = 3.4.
Use the TI calculator to construct the confidence interval. Press STAT and right arrow to TESTS. Use Stats because we have the summary statistics of the data. Enter the appropriate numbers and Calculate to get the confidence interval for the population mean.
Oct 20­7:16 AM
5
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
358/16. Construct 99% confidence interval to estimate population mean: n = 40, x­bar = 189, sigma = 87.
Oct 20­7:16 AM
Derive the formula for sample size from the margin of error formula.
Mar 22­9:37 AM
6
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
358/18. Find the sample size: E = 0.25, 99%, sigma = 2.5
Oct 20­7:16 AM
Derive the formula for sample size from the margin of error formula.
Mar 22­12:36 PM
7
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
358/20. Find the sample size: E = 1.5, 95%, sigma = 8.7
Oct 20­7:16 AM
Section 7.3 Estimating a Population Mean
358/22. Express the confidence interval in format x­bar – E < mu < x­bar + E.
Oct 20­7:16 AM
8
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
358/24. Write a statement that interprets the 95% confidence interval.
Oct 20­7:16 AM
Section 7.3 Estimating a Population Mean
359/26. Construct 99% confidence interval of mean : n = 150, mean = 37.1, sigma = 12.
Oct 20­7:16 AM
9
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
359/29. Construct 95% confidence interval of mean : n = 14, mean = 133.9, and assume sigma = 10.
Solution worked after class: 95% confidence interval uses alpha = 0.05 or alpha/2 = 0.025. This yields a critical value of z = 1.96. Use n = 14, sigma = 10, and z = 1.96 to get E = 5.2. The 95% confidence interval is (133.9 ­ 5.2, 133.9 + 5.2) or ( 128.7, 139.1).
Oct 20­7:16 AM
Section 7.3 Estimating a Population Mean
360/35. Find the sample size: 95%, E = 0.25, assume sigma = 10.6
Oct 20­7:16 AM
10
155S7.3.notebook
March 22, 2010
Section 7.3 Estimating a Population Mean
360/37. Find the sample size: 95%, E = 100, assume the values range from 12,000 to 70,000.
Solution worked after class: 95% confidence level yields z = 1.96 with E = 100 and sigma = (70000 ­ 12000) / 4 = 14500.
So, n = [1.96 * 14500 / 100]2 = 80769.64. Rounding n up to next whole number gives n = 80,770 as the desired sample size.
Oct 20­7:16 AM
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