What do you conclude about the data?

Group of answer choices

the calculated r value is not greater than the critical r value so the correlation is not significant.

the calculated r value is greater than the critical r value so the correlation is not significant.

the calculated r value is greater than the critical r value so the correlation is significant.

the calculated r value is not greater than the critical r value so the correlation is significant.

To determine the correct conclusion about the data, we need to compare the **calculated r value** (the correlation coefficient you computed from the data) with the **critical r value** (the threshold value for significance, based on the sample size and significance level, often from a statistical table).

Here’s how to interpret the options:

1. **If the calculated r value is greater than the critical r value**, the correlation is considered statistically significant (it indicates a real relationship between the variables).
   
2. **If the calculated r value is not greater than the critical r value**, the correlation is not statistically significant (it suggests the relationship could have occurred by chance).

Thus, the correct conclusion depends on the comparison between the two values. Here's how to interpret each statement:

- **"The calculated r value is not greater than the critical r value so the correlation is not significant."**  
   This is a possible correct conclusion if the calculated r value does not meet the threshold.

- **"The calculated r value is greater than the critical r value so the correlation is not significant."**  
   This is incorrect because a calculated r value greater than the critical r value indicates significance.

- **"The calculated r value is greater than the critical r value so the correlation is significant."**  
   This is the most likely correct conclusion when the r value exceeds the critical value, indicating statistical significance.

- **"The calculated r value is not greater than the critical r value so the correlation is significant."**  
   This is incorrect because a non-significant r value cannot indicate significance.

Therefore, the correct conclusion would most likely be:  
**"The calculated r value is greater than the critical r value so the correlation is significant."**

Would you like more details on how to interpret or calculate the r value and critical r value? 

Here are 5 related questions to explore:
1. How do you calculate the critical r value for a given sample size?
2. What does a correlation coefficient (r value) represent?
3. What factors influence the significance of a correlation?
4. What is the difference between a one-tailed and a two-tailed test for correlation?
5. How can you interpret a very small r value (close to 0)?

**Tip:** When in doubt, always check the sample size and significance level (usually 0.05) to determine the critical r value before making conclusions.

Learn how to interpret the results of a correlation test by comparing the calculated r value to the critical r value. This guide explains how to determine statistical significance and understand correlation in data. Suitable for high school students in Grades 11-12 studying statistics.

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