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Statistical Exercises with SAT Data

Statistical Exercises with SAT Data. Keri A. Catalfomo TriCounty Technical College. Empirical Rule Diagram for Females. 163. 275. 387. 499. 611. 723. 835. µ - 3 σ. µ - 2 σ. µ - 1 σ. µ. µ + 1 σ. µ + 2 σ. µ + 3 σ. Mean Math SAT Score. µ = 499 σ = 112. Calculating z-scores.

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Statistical Exercises with SAT Data

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  1. Statistical Exercises with SAT Data Keri A. Catalfomo TriCounty Technical College

  2. Empirical Rule Diagram for Females 163 275 387 499 611 723 835 µ - 3σ µ - 2σ µ - 1σ µ µ + 1σ µ + 2σ µ + 3σ Mean Math SAT Score µ = 499 σ = 112

  3. Calculating z-scores What was your Math SAT Score? Ex. Female student: Math SAT Score was 680 How many Standard Deviations is this from the mean? So, your score was 1.62 standard deviations above the mean.

  4. Empirical Rule Diagram for Females 680 (z = 1.62) 163 275 387 499 611 723 835 µ - 3σ µ - 2σ µ - 1σ µ µ + 1σ µ + 2σ µ + 3σ Mean Math SAT Score µ = 499 σ = 112

  5. Empirical Rule Diagram for Males 180 298 416 534 652 770 888 µ - 3σ µ - 2σ µ - 1σ µ µ + 1σ µ + 2σ µ + 3σ Mean Math SAT Score µ = 534 σ = 118

  6. Calculating z-scores What was your Math SAT Score? Ex. Male student: Math SAT Score was 720 How many Standard Deviations is this from the mean? So, your score was 1.58 standard deviations above the mean.

  7. Empirical Rule Females vs. Males Females Males 680 (z = 1.62) 720 (z = 1.58)

  8. Finding Probabilities Using the Normal Distribution P(Math SAT Score for a Male) > 720 534 720 x 0 1.58 z 1. Convert x = 720 to a z-value 2. P(x > 720) = P(z > 1.58) = 1 – P(z < 1.58) = 1 - .9429 = .0571 So, there are only 5.7% of students with a score above yours.

  9. Mean Math SAT Score vs. Student’s GPA Linear Correlation Hypothesis Test H0 : ρ = 0 – No Linear Correlation H1 : ρ ≠ 0 – Linear Correlation CV: r = ± .811 (α = .05, n = 6) TS: r = .987 Do Not Reject H0 α = .05 α = .05 -.811 .811 TS = .987 Decision: Reject H0 Conclusion: There is a Linear Correlation between Mean Math SAT Scores and Student’s GPA

  10. Mean Math SAT Score vs. Household Income Linear Correlation Hypothesis Test H0 : ρ = 0 – No Linear Correlation H1 : ρ ≠ 0 – Linear Correlation CV: r = ± .632 (α = .05, n = 10) TS: r = .967 Do Not Reject H0 α = .05 α = .05 -.632 .632 TS = .967 Decision: Reject H0 Conclusion: There is a Linear Correlation between Mean Math SAT Scores and Family Income

  11. For further information, contact me at: Keri A. Catalfomo kcatalfo@tctc.edu (864) 646-1621

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