This is the formula for
[ Select ]
Pearson’s r correlation
z-test for a sample mean
z-test for an individual score
effect size
.

Question

This is the formula for 
[ Select ]
Pearson’s r correlation
z-test for a sample mean
z-test for an individual score
effect size
 .

BlackTom AI · Accepted Answer

The prompt displays a standard z-score formula, z = (X − μ) / σ, and asks which formula this corresponds to.
Option 1: Pearson’s r correlation. This option is not correct because r is a measure of linear association between two variables, and its formula involves covariance and standard deviations, not the standard z-score transformation of a single observation.
Option 2: z-test for a sample mean. This test uses the same z statistic form, but specifically for testing a sample mean against a population mean, typically with the standard error (σ/√n) in the denominator when σ is known. The formula in the image uses σ in the denominator with a single X, not the standard error term that includes the sample size, so this is not the match here.
Option 3: z-test for an individual score. This is the correct context for a single observation standardized by the population mean and population standard deviation, yielding z = (X − μ)/σ. The formula shown directly corresponds to converting an individual score into a z-score.
Option 4: effect size. While z can relate to effect size in some contexts, the classic z-score formula shown is specifically the standardized score for an individual observation, not a generic effect-size measure like Cohen’s d or other effect-size indices. The direct substitution is not describing an effect size itself.

11398 SEM-2 2025 BRUCE ON-CAMPUS AND SEM-2 2025 BRUCE REALTIME Final Exam (Remotely Proctored)

This is the formula for [ Select ] Pearson’s r correlation z-test for a sample mean z-test for an individual score effect size .

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