Final answer:
The calculated t-score, representing the difference between two independent sample means in terms of standard errors, is approximately 1.201.
Step-by-step explanation:
The question involves using the t-score formula to determine the statistical significance of the difference between two independent sample means. Given that the difference between the sample means (X₁ - X₂) is 6.24 and the variance of the difference (s²difference) is 27, we can calculate the t-score by dividing the difference by the standard error, which is the square root of the variance of the difference. The standard error (SE) is thus √27 which equals 5.196.
The t-score is calculated as follows:
T = (X₁ - X₂) / SE = 6.24 / 5.196 ≈ 1.201
This t-score represents how many standard errors the difference between the two sample means is away from zero. If the t-score is large in absolute value, it suggests a significant difference between the group means.