A student was interested in examining whether there was a relationship between the amount of time studying (in minutes) and the grade received on an exam (on a 0 to 100 scale). The amount of time spent studying (examprep) and the final grade on the exam (grade) for 25 students is reported and recorded in SPSS.and perform the appropriate analyses to answer the questions below. The variables are named examprep and grade. a) State the null and alternative hypothesis. b) State a research question for the data. c) Calculate the correlation coefficient between the two variables in SPSS. What is the value of the correlation? d) Is the correlation significant? Test at α = .05. e) What is the effect size for the study? Would you characterize the effect size as small, medium, or large? f) Write the results of the study using APA format as appropriate.

To examine the relationship between study time and exam grade, here’s a breakdown of each step to approach this statistical analysis. The steps include hypothesis formulation, research question, calculation of the correlation coefficient, significance testing, effect size interpretation, and writing up results.

### a) State the Null and Alternative Hypothesis
- **Null Hypothesis (H₀):** There is no significant correlation between time spent studying (examprep) and exam grade (grade).
  \[
  H₀: \rho = 0
  \]
- **Alternative Hypothesis (Hₐ):** There is a significant correlation between time spent studying (examprep) and exam grade (grade).
  \[
  Hₐ: \rho \neq 0
  \]

### b) State a Research Question for the Data
- **Research Question:** Is there a relationship between the amount of time students spend studying for an exam and their resulting exam grade?

### c) Calculate the Correlation Coefficient between the Two Variables in SPSS
To calculate the Pearson correlation coefficient (r) between `examprep` and `grade` in SPSS:
1. Open the dataset in SPSS.
2. Go to **Analyze > Correlate > Bivariate**.
3. Move both variables, `examprep` and `grade`, into the **Variables** box.
4. Ensure **Pearson** is checked under **Correlation Coefficients**.
5. Set **Test of Significance** to **Two-tailed** and press **OK**.

After this, SPSS will output a correlation coefficient. Let’s assume the value of the correlation coefficient (r) is **0.67**. This value may vary based on the actual data.

### d) Is the Correlation Significant? Test at α = .05
In the SPSS output, you will see a p-value associated with the correlation coefficient. To test the significance:
- Compare the p-value to α = 0.05.
  - If **p < 0.05**, the correlation is significant.
  - If **p ≥ 0.05**, the correlation is not significant.
  
Assuming the p-value is **0.001** (for illustration), this would indicate that the correlation is statistically significant, meaning we can reject the null hypothesis.

### e) What is the Effect Size for the Study? Would You Characterize the Effect Size as Small, Medium, or Large?
The **effect size** for correlation is interpreted directly by the correlation coefficient (r):
- **Small effect**: |r| = 0.10 to 0.29
- **Medium effect**: |r| = 0.30 to 0.49
- **Large effect**: |r| ≥ 0.50

Given an r = 0.67, this would be classified as a **large effect size**.

### f) Write the Results of the Study Using APA Format as Appropriate
Here is a sample APA-style report of the results:

> A Pearson correlation was conducted to examine the relationship between the amount of time students spent studying for an exam and their final exam grades. The analysis revealed a statistically significant positive correlation between study time and exam grade, \( r(23) = 0.67, p = 0.001 \). This suggests that students who spent more time studying tended to receive higher grades on the exam. The effect size, represented by the correlation coefficient, indicates a large effect (Cohen, 1988), implying a strong association between the variables in this sample.

Would you like further details or have any questions?

---

### 5 Related Questions for Further Exploration:
1. How can we determine if there is causation between study time and exam grades, not just correlation?
2. What other factors might influence exam grades, and how could these be measured?
3. If the correlation was not significant, what steps might be taken to further investigate the data?
4. How would you interpret a negative correlation in a similar study?
5. How could effect size influence decisions in educational policies?

---

### Tip:
When interpreting a correlation, remember it only shows association, not causation. Factors like motivation or prior knowledge could also affect both study time and exam performance, potentially influencing the correlation.

A student was interested in examining whether there was a relationship between the amount of time studying (in minutes) and the grade received on an exam (on a 0 to 100 scale). The amount of time spent studying (examprep) and the final grade on the exam (grade) for 25 students is reported and recorded in SPSS. Perform the appropriate analyses to answer the questions below. The variables are named examprep and grade. a) State the null and alternative hypothesis. b) State a research question for the data. c) Calculate the correlation coefficient between the two variables in SPSS. What is the value of the correlation? d) Is the correlation significant? Test at α = .05. e) What is the effect size for the study? Would you characterize the effect size as small, medium, or large? f) Write the results of the study using APA format as appropriate.

Explore how to use SPSS to analyze the relationship between study time and exam grades using Pearson correlation. This detailed guide covers hypothesis formulation, calculating correlation coefficients, testing significance at α = 0.05, and interpreting effect size with APA-style reporting. Suitable for undergraduate-level statistics courses.

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