Statistical Exercises with SAT Data

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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. - PowerPoint PPT Presentation

Transcript of Statistical Exercises with SAT Data

  • Keri A. CatalfomoTriCounty Technical College

  • Empirical Rule Diagram for FemalesMean Math SAT Score = 499 = 112163387499275835723611 + 1 + 2 - 3 - 2 - 1 + 3

  • 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.Calculating z-scores

  • Empirical Rule Diagram for FemalesMean Math SAT Score = 499 = 112163387499275835723611 + 1 + 2 - 3 - 2 - 1 + 3 680 (z = 1.62)

  • Empirical Rule Diagram for MalesMean Math SAT Score = 534 = 118180416534298888770652 + 1 + 2 - 3 - 2 - 1 + 3

  • 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.Calculating z-scores

  • Empirical Rule Females vs. Males Females Males680 (z = 1.62)720 (z = 1.58)

  • P(Math SAT Score for a Male) > 720Finding Probabilities Using the Normal Distribution2. 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. 1. Convert x = 720 to a z-value 720 x 1.58 z 534 0

  • H0 : = 0 No Linear Correlation

    H1 : 0 Linear Correlation

    CV: r = .811 ( = .05, n = 6)

    TS: r = .987

    Decision: Reject H0

    Conclusion: There is a Linear Correlation between Mean Math SAT Scores and Students GPAMean Math SAT Score vs. Students GPALinear Correlation Hypothesis Test = .05 = .05-.811 .811Do Not Reject H0 TS = .987

  • H0 : = 0 No Linear Correlation

    H1 : 0 Linear Correlation

    CV: r = .632 ( = .05, n = 10)

    TS: r = .967

    Decision: Reject H0

    Conclusion: There is a Linear Correlation between Mean Math SAT Scores and Family IncomeMean Math SAT Score vs. Household IncomeLinear Correlation Hypothesis Test = .05 = .05-.632 .632Do Not Reject H0 TS = .967

  • For further information, contact me at:

    Keri A. Catalfomo

    kcatalfo@tctc.edu

    (864) 646-1621

    e*e*e*