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Answer: 5.25, calculated correctly using the formula for a parametric test of correlation.
### Explanation **Correct Answer: B (5.25)** For a parametric test of correlation, assuming the variables are normally distributed, the t-statistic is calculated as: \[ t = \frac{r \sqrt{n - 2}}{\sqrt{1 - r^2}} \] Where: - \( r \) is the sample correlation coefficient (0.6). - \( n \) is the sample size (51). Substituting the values: \[ t = \frac{0.6 \times \sqrt{51 - 2}}{\sqrt{1 - 0.6^2}} = \frac{0.6 \times 7}{\sqrt{1 - 0.36}} = \frac{4.2}{0.8} = 5.25 \] **Why Not A or C?** - **A (0.07):** This incorrect result occurs if the numerator and denominator are swapped in the formula. - **C (6.64):** This arises if the correlation coefficient \( r \) is not squared in the denominator, leading to an incorrect calculation.
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In a parametric test examining the correlation between two variables, given a sample size of 51 and a sample correlation of 0.6, the t-statistic is most likely:
A
0.07, which would result from incorrectly swapping the numerator and denominator in the formula.
B
5.25, calculated correctly using the formula for a parametric test of correlation.
C
6.64, arising from omitting the squaring of the correlation coefficient in the denominator.
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