Questions: For a data set of brain volumes (cm^3) and IQ scores of nine males, the linear correlation coefficient is found and the P-value is 0.238. Write a statement that interprets the P-value and includes a conclusion about linear correlation.

For a data set of brain volumes (cm^3) and IQ scores of nine males, the linear correlation coefficient is found and the P-value is 0.238. Write a statement that interprets the P-value and includes a conclusion about linear correlation.

Transcript text: For a data set of brain volumes $\left(\mathrm{cm}^{3}\right)$ and IQ scores of nine males, the linear correlation coefficient is found and the P-value is 0.238. Write a statement that interprets the P-value and includes a conclusion about linear correlation.

Solution

Step 1: Calculate the Linear Correlation Coefficient (r)

The linear correlation coefficient (r) is calculated based on the data and is given as None. It quantifies the strength and direction of the linear relationship between the two variables.

Step 2: Calculate the P-value

The P-value is determined to be 0.238, which represents the probability of observing a correlation coefficient at least as extreme as the one calculated, under the null hypothesis that there is no linear correlation between the variables.

Step 3: Interpret the P-value

Since the P-value (0.238) is greater than the significance level (α = 0.05), there is insufficient evidence to reject the null hypothesis. Therefore, it cannot be concluded that a significant linear correlation exists between the variables.

Conclusion

Based on the P-value (0.238) and the predetermined significance level (α = 0.05), there is insufficient evidence to assert that a significant linear correlation exists between the two variables under study.

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