Correlation Hypothesis Test Example: Pearson Correlation Quiz and Flashcards

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.

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.