Although their formulas are similar, one primary difference between a z-score (z) and a t-statistic (t) is that the ______ of the formula for the t-statistic involves ______.
A) denominator; the variability of individual scores (Xs), not the variability of sample means
B) numerator; difference between a score (
X) and a population mean (μ)
C) denominator; the variability of sample means , not the variability of individual scores (Xs)
D) numerator; the difference between a score (
X) and a sample mean

Question

Although their formulas are similar, one primary difference between a z-score (z) and a t-statistic (t) is that the ______ of the formula for the t-statistic involves ______.
A) denominator; the variability of individual scores (Xs), not the variability of sample means 
B) numerator; difference between a score (
X) and a population mean (μ) 
C) denominator; the variability of sample means , not the variability of individual scores (Xs) 
D) numerator; the difference between a score (
X) and a sample mean

Quizplus · Accepted Answer

The denominator of the formula for the t-statistic involves the variability of sample means, not the variability of individual scores (Xs) as in the z-score formula. This is because the t-statistic is used when we do not know the population standard deviation, and therefore need to estimate it using the sample standard deviation, which introduces additional variability into the calculation. The numerator of the t-statistic formula still involves the difference between a score (X) and a sample mean, as in the z-score formula.

Although Their Formulas Are Similar, One Primary Difference Between a Z-Score