Statistics and Probability Estimation of Parameters pptx
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The document discusses estimation in statistics, specifically how to infer population parameters using sample data. It explains types of population estimates, such as point and interval estimates, and provides examples of calculating averages and variances for given student grades. The document also includes a formula for standard error when estimating the population mean.
Statistics and Probability Estimation of Parameters pptx
- 1. Estimation of Parameters Statistics and Probability
- 2. Descripted measures computed from a sample. Statistic Parameters Descripted measures computed from a population.
- 3. Questions
- 4. 1. What do we call a process by which one makes inferences about a population based on observation obtained from a sample?
- 5. 2. What do we call the value or range of values used to approximate a parameter?
- 6. 3. What are the types of population Estimate?
- 7. 1. What do we call a process by which one makes inferences about a population based on observation obtained from a sample? ----ESTIMATION---- -Process used to calculate the population parameters by analyzing only a small random sample from the population
- 8. 2. What do we call the value or range of values used to approximate a parameter? ----ESTIMATE----
- 9. 3. What are the types of population Estimate? A. Point Estimate B. Interval Estimate
- 10. 3. What are the types of population Estimate? A. Point Estimate -a point estimate of a population parameter is a single value of a statistics
- 11. 3. What are the types of population Estimate? B. Interval Estimate -range of values within which the parameter values possibly falls.
- 12. Point Estimate -it is used to represent the true value of a parameter. --Example-- sample mean estimates of the population mean. Sample variance estimates the population variance. 𝑥 = 𝑥 𝑛 𝑠2 = 𝑥 − 𝑥 2 𝑛 − 1
- 13. Point Estimate A researcher wants to estimate the average grade of all mathematics students in Saint Joseph Institute of Technology. He determined the grades of five students as follows; 76, 82, 88, 90 & 96. Estimate the average mathematics grades of all the students and the variance of their grades. 𝑥 = 𝑥 𝑛 𝑠2 = 𝑥 − 𝑥 2 𝑛 − 1 𝜎𝑚 = 𝜎 𝑛
- 14. Point Estimate A researcher wants to estimate the average grade of all mathematics students in Saint Joseph Institute of Technology. He determined the grades of five students as follows; 76, 82, 88, 90 & 96. Estimate the average mathematics grades of all the students and the variance of their grades. 𝑥 = 𝑥 𝑛 𝑥 = 76 + 82 + 88 + 90 + 96 5 𝑥 = 432 5 𝑥 = 86.4 ∴ 𝒕𝒉𝒆 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒎𝒆𝒂𝒏 𝒊𝒔 𝟖𝟔. 𝟒
- 15. Point Estimate 𝑠2 = 𝑥 − 𝑥 2 𝑛 − 1 𝑠2 = 76 − 86.4 2 + 82 − 86.4 2 + 88 − 86.4 2 + 90 − 86.4 2 + 96 − 86.4 2 5 − 1 𝑠2 = −10 2 + −4.4 2 + 1.6 2 + 3.6 2 + 9.6 2 4 𝑠2 = 108.16 + 19.36 + 2.56 + 12.96 + 92.16 4 𝑠2 = 235.2 4 𝑠2 = 58.8 𝑻𝒉𝒖𝒔, 𝒕𝒉𝒆 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆 𝒊𝒔 𝟓𝟖. 𝟖
- 16. Point Estimate What is the best point estimate of the population mean 𝜇 if a sample consisting of 19, 20, 26, 29, 𝑎𝑛𝑑 36 and is obtained from the population? 𝑥 = 𝑥 𝑛 𝑠2 = 𝑥 − 𝑥 2 𝑛 − 1 𝜎𝑚 = 𝜎 𝑛
- 17. Point Estimate What is the best point estimate of the population mean 𝜇 if a sample consisting of 19, 20, 26, 29, 𝑎𝑛𝑑 36 and is obtained from the population? 𝑥 = 𝑥 𝑛 𝑥 = 19 + 20 + 26 + 29 + 36 5 𝑥 = 130 5 𝑥 = 26 ∴ 𝒕𝒉𝒆 𝒃𝒆𝒔𝒕 𝒑𝒐𝒊𝒏𝒕 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒎𝒆𝒂𝒏 𝒊𝒔 𝟐𝟔
- 18. Point Estimate A sample consisting of 12,14,18,22 𝑎𝑛𝑑 24 is used to estimate the population mean 𝜇 . What is the standard error of the point estimate of the population mean 𝜇 when the population standard deviation is estimated to be 𝜎 = 3.25? 𝑥 = 𝑥 𝑛 𝑠2 = 𝑥 − 𝑥 2 𝑛 − 1 𝜎𝑚 = 𝜎 𝑛
- 19. Point Estimate A sample consisting of 12,14,18,22 𝑎𝑛𝑑 24 is used to estimate the population mean 𝜇 . What is the standard error of the point estimate of the population mean 𝜇 when the population standard deviation is estimated to be 𝜎 = 3.25? 𝜎𝑚 = 𝜎 𝑛 𝜎𝑚 = 3.25 5 𝜎𝑚 = 3.25 2.24 𝜎𝑚 = 1.45 ∴ 𝒕𝒉𝒆 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒆𝒓𝒓𝒐𝒓 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒐𝒊𝒏𝒕 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝒊𝒔 𝟏. 𝟒𝟓
- 20. Point Estimate 𝑥 = 𝑥 𝑛 𝑠2 = 𝑥 − 𝑥 2 𝑛 − 1 𝜎𝑚 = 𝜎 𝑛
- 21. Point Estimate 𝑥 = 𝑥 𝑛 𝑠2 = 𝑥 − 𝑥 2 𝑛 − 1 𝜎𝑚 = 𝜎 𝑛
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