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- 7. S.D ( σ ) = = Σ(X –X) 2 / n-1 =(√1924/ (12-1) _____ = √174 = 13.2 10/01/11 STATISTICS Observation (X) __ Mean ( X ) _ Deviation (X- X) __ (X-X) 2 58 __ X = Σ X / n = 984/12 = 82 -12 576 66 -16 256 70 -12 144 74 -8 64 80 -2 4 86 -4 16 90 8 64 100 18 324 79 -3 9 96 14 196 88 6 36 97 15 225 Σ X = 984 _ Σ (X - X) 2 =1914
- 8. x The Empirical Rule (applies to bell-shaped distributions ) FIGURE 2-15 10/01/11 STATISTICS
- 9. x - s x x + s 68% within 1 standard deviation 34% 34% The Empirical Rule (applies to bell-shaped distributions ) FIGURE 2-15 10/01/11 STATISTICS
- 10. x - 2s x - s x x + 2s x + s 68% within 1 standard deviation 34% 34% 95% within 2 standard deviations The Empirical Rule (applies to bell-shaped distributions ) 13.5% 13.5% FIGURE 2-15 10/01/11 STATISTICS
- 11. x - 3s x - 2s x - s x x + 2s x + 3s x + s 68% within 1 standard deviation 34% 34% 95% within 2 standard deviations 99.7% of data are within 3 standard deviations of the mean The Empirical Rule (applies to bell-shaped distributions ) 0.1% 2.4% 2.4% 13.5% 13.5% FIGURE 2-15 10/01/11 STATISTICS 0.1%
- 17. Areas within 1 & 2 S.D's of the Mean ( Mean-36, SD-8) and (Mean-70, SD-3) 10/01/11 STATISTICS
- 22. Tests of Significance DATA Discrete (Qualitative) Continuous Non- Parametric Test Chi- square, Fishers exact sign, Mann Whitney Parametric Tests Z-test, t-test ANOVA test 10/01/11 STATISTICS
- 26. Calculated value 13.99 > tabulated Value 3.84 Null hypothesis rejected Conclusion:- Treatment A more effective than Treatment B Expected value ג 2 =∑ (O-E) 2 E (90-78) 2 + (10-22) 2 +( 105-117) 2 +( 45-33 ) 2 78 22 117 33 = 13.99 T/t Outcome Total Cure NotCured A 78 22 100 B 117 33 150 Total 195 55 250
- 30. Convenience Sampling - use results that are readily available 10/01/11 STATISTICS
- 31. Random Sampling - selection so that each has an equal chance of being selected 10/01/11 STATISTICS
- 32. Systematic Sampling - Select some starting point and then select every K th element in the population 10/01/11 STATISTICS
- 33. Stratified Sampling - subdivide the population into subgroups that share the same characteristic, then draw a sample from each stratum 10/01/11 STATISTICS
- 34. Cluster Sampling - divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters 10/01/11 STATISTICS
- 36. a c e b d 10/01/11 STATISTICS
- 38. SAMPLING ERRORS 10/01/11 STATISTICS Population Conclusion based on sample Null hypothesis Null hypothesis Rejected Accepted Null hypothesis True Type 1 error Correct decision Null hypothesis False Correct decision Type 2 error
Notas del editor
- page 79 of text
- Some student have difficulty understand the idea of ‘within one standard deviation of the mean’. Emphasize that this means the interval from one standard deviation below the mean to one standard deviation above the mean.
- These percentages will be verified by the concepts learned in Chapter 5. Emphasize the Empirical Rule is appropriate for data that is in a BELL-SHAPED distribution.
- page 19 of text
- Students will most often confuse stratified sampling with cluster sampling. Both break the population into strata or sections. With stratified a few are selected from each strata. With cluster, choose a few of the strata and choose all the member from the chosen strata.
- page 23 of text