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Reinforcing the 68-95-99.7 Rule

Reinforcing the 68-95-99.7 Rule. Process. Survey data on 391 students Used the Verbal SAT scores Processed the information using MiniTab 15…. Results. Mean: 591.84 Standard Deviation: 73.24. Verbal Z-scores. Took Verbal SAT scores column (Verbal SAT - mean) / s.d.

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Reinforcing the 68-95-99.7 Rule

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  1. Reinforcing the 68-95-99.7 Rule

  2. Process • Survey data on 391 students • Used the Verbal SAT scores • Processed the information using MiniTab 15…

  3. Results • Mean: 591.84 • Standard Deviation: 73.24

  4. Verbal Z-scores • Took Verbal SAT scores column • (Verbal SAT - mean) / s.d. • …created VerbalZ column -Created histograms comparing the two

  5. Histogram of Verbal SAT scores • Shows fairly normal shape • Now, compare it to the histogram displaying the VerbalZ scores… • Will it be the same shape? • Any differences?

  6. What if we superimposed the VerbalZ histogram over the Verbal histogram?

  7. VerbalZ vs Verbal

  8. Note the discrepancy between the two near the mean… • “The discrepancy has to do with the choices MiniTab makes about what interval midpoints to use” - Prof. Pfenning

  9. Count • <-3 =2/391 • (-3,-2) =5/391 • (-2,-1) =47/391 • (-1, 0) =146/391 • (0,1) =130/391 • (1,2) =49/391 • (2,3) =12/391 • >3 =0/391

  10. Proportion of Standardized Values • -3 to +3 = .995 • -2 to +2 = .951 • -1 to +1 = .706

  11. Observed vs. Expected • -3 to +3 = .995 vs .997 • -2 to +2 = .951 vs .95 • -1 to +1 = .706 vs .68 • So… it appears to be fairly normal

  12. 90-95-98-99 Rule • .90 that Z takes a value (-1.645,1.645) • .95 that Z takes a value (-1.960, 1.960) • .98 that Z takes a value (-2.326, 2.326) • .99 that Z takes a value (-2.576, 2.576)

  13. Results for Verbal SATs • .910 that Z takes a value (-1.645, 1.645) • .969 that Z takes a value (-2.326, 2.326) • .979 that Z takes a value (-2.576, 2.576) - How well does this conform to a perfect curve?

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