Hypothesis Tests with Pearson Correlation: Example
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Questions and Answers

What is the formula for calculating SS for Hours?

  • Σ(X - M- )^3
  • Σ(X - M- )/ (correct)
  • Σ(X - M- )*
  • Σ(X - M- )^2

    • What is the value of SP when calculating Correlation Hypothesis Test?

  • 3516.49
  • 4820.1
  • 359097.45
  • 535.5 (correct)

    • How is the correlation coefficient (r) calculated?

  • SS? / SP
  • SP / SS?
  • SP / SS- (correct)
  • SS- / SP

    • What is the value of t in the Directional Hypothesis Test?

    <p>5.56</p> Signup and view all the answers

    What is the decision made in the Hypothesis Test?

    <p>Reject the null hypothesis</p> Signup and view all the answers

    What is the relationship between the number of hours slept and test performance?

    <p>There is a significant, strong, positive relationship</p> Signup and view all the answers

    What is the complete t statistic formula for hypothesis tests with the Pearson correlation?

    <p>𝑡 = 𝑟 − 𝜌 (1 − 𝑟^2) (𝑛 − 2)</p> Signup and view all the answers

    What is the null hypothesis in the correlation hypothesis test example?

    <p>𝜌 = 0</p> Signup and view all the answers

    What is the alternative hypothesis in the correlation hypothesis test example?

    <p>𝜌 ≠ 0</p> Signup and view all the answers

    What is the alpha level in the correlation hypothesis test example?

    <p>𝛼 =.05</p> Signup and view all the answers

    What is the critical region for the correlation hypothesis test example?

    <p>±8.549</p> Signup and view all the answers

    What is the value of 𝑑𝑓 (𝒏 − 𝟐) in the correlation hypothesis test example?

    <p>8</p> Signup and view all the answers

    Study Notes

    Correlation Hypothesis Test

    • A researcher is interested in examining the relationship between the number of hours of sleep students get the night before an exam and their exam scores.

    Step 1: State the Hypotheses and Select an Alpha Level

    • Null Hypothesis: 𝜌 = 0 (no correlation between hours slept and test scores)
    • Alternative Hypothesis: 𝜌 ≠ 0 (there is a correlation between hours slept and test scores)
    • Alpha Level: 𝛼 =.05 (significance level)

    Step 2: Locate the Critical Region

    • Degrees of Freedom (df): 𝑛 − 2 = 10 − 2 = 8
    • Critical Region: One-Tailed Test (𝛼 =.05, df = 8, critical t-value = 1.859)

    Step 3: Calculate the Test Statistic

    • Calculate SS (Sum of Squares) for X and Y:
      • SS for Hours: 𝑆𝑆"#$%& = 74.5
      • SS for Scores: 𝑆𝑆 = 4820.1
    • Calculate SP (Sum of Cross Products): 𝑆𝑃 = 535.5
    • Calculate r (correlation coefficient): 𝑟 = 𝑆𝑃 / √(𝑆𝑆"#$%& × 𝑆𝑆) = 0.89
    • Calculate t (t-statistic): 𝑡 = 𝑟 / √(1 - 𝑟^2) / (𝑛 - 2) = 5.56

    Step 4: Make a Decision

    • Since |𝑟| > 𝑟 critical and 𝑡 > 𝑡 critical, reject the null hypothesis.
    • There is a significant, strong, positive relationship between the number of hours slept and test performance.

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    Description

    This quiz focuses on conducting a hypothesis test using the Pearson correlation coefficient formula. In this example, the relationship between the number of hours of sleep students get before an exam and their exam scores is examined with a sample of 10 first-year psychology students.

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