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Questions and Answers
What is the formula for calculating SS for Hours?
What is the formula for calculating SS for Hours?
What is the value of SP when calculating Correlation Hypothesis Test?
What is the value of SP when calculating Correlation Hypothesis Test?
How is the correlation coefficient (r) calculated?
How is the correlation coefficient (r) calculated?
What is the value of t in the Directional Hypothesis Test?
What is the value of t in the Directional Hypothesis Test?
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What is the decision made in the Hypothesis Test?
What is the decision made in the Hypothesis Test?
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What is the relationship between the number of hours slept and test performance?
What is the relationship between the number of hours slept and test performance?
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What is the complete t statistic formula for hypothesis tests with the Pearson correlation?
What is the complete t statistic formula for hypothesis tests with the Pearson correlation?
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What is the null hypothesis in the correlation hypothesis test example?
What is the null hypothesis in the correlation hypothesis test example?
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What is the alternative hypothesis in the correlation hypothesis test example?
What is the alternative hypothesis in the correlation hypothesis test example?
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What is the alpha level in the correlation hypothesis test example?
What is the alpha level in the correlation hypothesis test example?
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What is the critical region for the correlation hypothesis test example?
What is the critical region for the correlation hypothesis test example?
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What is the value of 𝑑𝑓 (𝒏 − 𝟐) in the correlation hypothesis test example?
What is the value of 𝑑𝑓 (𝒏 − 𝟐) in the correlation hypothesis test example?
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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.
