In Case 2B, which expression defines Tcalc?

In Case 2B, which expression defines Tcalc?

• A. (mean1 - mean2) / sqrt((s1^2/n1)+(s2^2/n2))
• B. (mean1 - mean2) / sqrt(s1^2/n1)
• C. (Icalculated mean 1-calculated mean 2I)/ sqrt((s1^2/n1)+(s2^2/n2))
• D. (Icalculated mean 1-calculated mean 2I)/ sqrt((s1^2/n1)+(s2^2/n2))

Answer: (D)

Tcalc measures how far apart the observed means are compared to how much variability there is in the two samples. For independent samples, the standard error of the difference is the square root of the sum of the two variances each divided by its sample size: sqrt(s1^2/n1 + s2^2/n2). The statistic uses the absolute difference in means divided by that standard error, giving Tcalc = |mean1 − mean2| / sqrt(s1^2/n1 + s2^2/n2). The absolute value reflects the magnitude of the difference, which is what’s compared to the t-distribution in a two-tailed test, and the denominator must include both s1^2/n1 and s2^2/n2 to account for uncertainty from both samples. Using only one term in the denominator would ignore part of the variability, so the expression that matches this form is the correct one.

Tcalc measures how far apart the observed means are compared to how much variability there is in the two samples. For independent samples, the standard error of the difference is the square root of the sum of the two variances each divided by its sample size: sqrt(s1^2/n1 + s2^2/n2). The statistic uses the absolute difference in means divided by that standard error, giving Tcalc = |mean1 − mean2| / sqrt(s1^2/n1 + s2^2/n2). The absolute value reflects the magnitude of the difference, which is what’s compared to the t-distribution in a two-tailed test, and the denominator must include both s1^2/n1 and s2^2/n2 to account for uncertainty from both samples. Using only one term in the denominator would ignore part of the variability, so the expression that matches this form is the correct one.