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Population Total Estimation Methods in Statistics

Learn about finite population procedures for estimating the total population using sampling with or without replacement. Understand expected value, variance, standard deviation, and standard error in this context.

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Population Total Estimation Methods in Statistics

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  1. Chapter 3Selected Basic Concepts in Statistics, Part 2 • Estimating a Population Total  • Finite Population Procedures

  2. Estimating the population total 

  3. Estimating the population total  • Expected value

  4. Estimating the population total  • Variance, standard deviation, standard error

  5. Finite population case • Example: sampling w/ replacement to estimate 

  6. Finite population case • Example: sampling w/ replacement to estimate 

  7. Finite population case • Example: sampling w/ replacement to estimate  • From the table:

  8. Finite population case • Example: sampling w/ replacement to estimate 

  9. Finite population case • Example: sampling w/ replacement to estimate  • Example Summary

  10. Finite population case • Sampling w/ replacement to estimate pop. total  • In general

  11. Finite population case • Sampling w/ replacement to estimate pop. total 

  12. Finite population case In reality, do not know value of yifor every item in the population. BUT can choose i proportional to a known measurement highly correlated with yi . • Sampling w/ replacement to estimate pop. total 

  13. Finite population case • Sampling w/ replacement to estimate pop. total 

  14. Finite population case Thus far we have assumed a population that does not change when the first item is selected, that is, we sampled with replacement. • Sampling without replacement to estimate pop. total  When sampling without replacement this is not true • Example: population {1, 2, 3, 4}; n=2, suppose equally likely. • Prob. of selecting 3 on first draw is ¼. • Prob. of selecting 3 on second draw depends on first draw (probability is 0 or 1/3)

  15. Finite population case • Sampling without replacement to estimate pop. total  Worksheet

  16. End of Chapter 3, part 2

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