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Basic Business Statistics 8th Edition

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Basic Business Statistics 8th Edition

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    1. © 2002 Prentice-Hall, Inc. Chap 8-1 Basic Business Statistics (8th Edition) Chapter 8 Confidence Interval Estimation

    2. © 2002 Prentice-Hall, Inc. Chap 8-2 Chapter Topics Estimation process Point estimates Interval estimates Confidence interval estimation for the mean ( known) Determining sample size Confidence interval estimation for the mean ( unknown)

    3. © 2002 Prentice-Hall, Inc. Chap 8-3 Chapter Topics Confidence interval estimation for the proportion Confidence interval estimation for population total Confidence interval estimation for total difference in the population Estimation and sample size determination for finite population Confidence interval estimation and ethical considerations

    4. © 2002 Prentice-Hall, Inc. Chap 8-4 Estimation Process

    5. © 2002 Prentice-Hall, Inc. Chap 8-5 Point Estimates

    6. © 2002 Prentice-Hall, Inc. Chap 8-6 Interval Estimates Provides range of values Takes into consideration variation in sample statistics from sample to sample Is based on observation from one sample Gives information about closeness to unknown population parameters Is stated in terms of level of confidence Never 100% certain

    7. © 2002 Prentice-Hall, Inc. Chap 8-7 Confidence Interval Estimates

    8. © 2002 Prentice-Hall, Inc. Chap 8-8 Confidence Interval for ( Known) Assumptions Population standard deviation is known Population is normally distributed If population is not normal, use large sample Confidence interval estimate

    9. © 2002 Prentice-Hall, Inc. Chap 8-9 Elements of Confidence Interval Estimation Level of confidence Confidence in which the interval will contain the unknown population parameter Precision (range) Closeness to the unknown parameter Cost Cost required to obtain a sample of size n

    10. © 2002 Prentice-Hall, Inc. Chap 8-10 Level of Confidence Denoted by A relative frequency interpretation In the long run, of all the confidence intervals that can be constructed will contain the unknown parameter A specific interval will either contain or not contain the parameter No probability involved in a specific interval

    11. © 2002 Prentice-Hall, Inc. Chap 8-11 Interval and Level of Confidence

    12. © 2002 Prentice-Hall, Inc. Chap 8-12 Factors Affecting Interval Width (Precision) Data variation Measured by Sample size Level of confidence

    13. © 2002 Prentice-Hall, Inc. Chap 8-13 Determining Sample Size (Cost)

    14. © 2002 Prentice-Hall, Inc. Chap 8-14 Determining Sample Size for Mean What sample size is needed to be 90% confident of being correct within ± 5? A pilot study suggested that the standard deviation is 45.

    15. © 2002 Prentice-Hall, Inc. Chap 8-15 Determining Sample Size for Mean in PHStat PHStat | sample size | determination for the mean … Example in excel spreadsheet

    16. © 2002 Prentice-Hall, Inc. Chap 8-16 Assumptions Population standard deviation is unknown Population is normally distributed If population is not normal, use large sample Use student’s t distribution Confidence interval estimate Confidence Interval for ( Unknown)

    17. © 2002 Prentice-Hall, Inc. Chap 8-17 Student’s t Distribution

    18. © 2002 Prentice-Hall, Inc. Chap 8-18 Degrees of Freedom (df ) Number of observations that are free to vary after sample mean has been calculated Example: Mean of 3 numbers is 2

    19. © 2002 Prentice-Hall, Inc. Chap 8-19 Student’s t Table

    20. © 2002 Prentice-Hall, Inc. Chap 8-20 Example

    21. © 2002 Prentice-Hall, Inc. Chap 8-21 PHStat | confidence interval | estimate for the mean, sigma unknown Example in excel spreadsheet Confidence Interval for ( Unknown) in PHStat

    22. © 2002 Prentice-Hall, Inc. Chap 8-22 Confidence Interval Estimate for Proportion Assumptions Two categorical outcomes Population follows binomial distribution Normal approximation can be used if and Confidence interval estimate

    23. © 2002 Prentice-Hall, Inc. Chap 8-23 Example A random sample of 400 voters showed 32 preferred candidate A. Set up a 95% confidence interval estimate for p.

    24. © 2002 Prentice-Hall, Inc. Chap 8-24 Confidence Interval Estimate for Proportion in PHStat PHStat | confidence interval | estimate for the proportion … Example in excel spreadsheet

    25. © 2002 Prentice-Hall, Inc. Chap 8-25 Determining Sample Size for Proportion Out of a population of 1,000, we randomly selected 100, of which 30 were defective. What sample size is needed to be within ± 5% with 90% confidence?

    26. © 2002 Prentice-Hall, Inc. Chap 8-26 Determining Sample Size for Proportion in PHStat PHStat | sample size | determination for the proportion … Example in excel spreadsheet

    27. © 2002 Prentice-Hall, Inc. Chap 8-27 Confidence Interval for Population Total Amount Point estimate Confidence interval estimate

    28. © 2002 Prentice-Hall, Inc. Chap 8-28 Confidence Interval for Population Total: Example

    29. © 2002 Prentice-Hall, Inc. Chap 8-29 Example Solution

    30. © 2002 Prentice-Hall, Inc. Chap 8-30 Example Solution in PHStat PHStat | confidence intervals | estimate for the population total Excel spreadsheet for the voucher example

    31. © 2002 Prentice-Hall, Inc. Chap 8-31 Confidence Interval for Total Difference in the Population Point estimate Where is the sample average difference Confidence interval estimate Where

    32. © 2002 Prentice-Hall, Inc. Chap 8-32 Estimation for Finite Population Samples are selected without replacement Confidence interval for the mean ( unknown) Confidence interval for proportion

    33. © 2002 Prentice-Hall, Inc. Chap 8-33 Sample Size Determination for Finite Population Samples are selected without replacement When estimating the mean When estimating the proportion

    34. © 2002 Prentice-Hall, Inc. Chap 8-34 Ethical Considerations Report confidence interval (reflect sampling error) along with the point estimate Report the level of confidence Report the sample size Provide an interpretation of the confidence interval estimate

    35. © 2002 Prentice-Hall, Inc. Chap 8-35 Chapter Summary Illustrated estimation process Discussed point estimates Addressed interval estimates Discussed confidence interval estimation for the mean ( known) Addressed determining sample size Discussed confidence interval estimation for the mean ( unknown)

    36. © 2002 Prentice-Hall, Inc. Chap 8-36 Chapter Summary Discussed confidence interval estimation for the proportion Addressed confidence interval estimation for population total Discussed confidence interval estimation for total difference in the population Addressed estimation and sample size determination for finite population Addressed confidence interval estimation and ethical issues

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