In the calculation of a $z$-score, what does the denominator of the test statistic measure?

• A. The mean of the sample
• B. The sum of all data values
• C. The standard deviation of the population $\sigma$
• D. The median of the population

Answer: (C)

Verified step by step guidance

1. Recall the formula for the z-score, which is given by: \[ z = \frac{X - \mu}{\sigma} \] where \(X\) is the observed value, \(\mu\) is the population mean, and \(\sigma\) is the denominator in question.
2. Understand that the numerator \((X - \mu)\) measures how far the observed value is from the population mean.
3. Focus on the denominator \(\sigma\), which is the standard deviation of the population. This measures the average amount of variability or dispersion of the data points around the mean.
4. Recognize that dividing by the standard deviation standardizes the difference, allowing comparison across different scales or units.
5. Therefore, the denominator in the z-score formula measures the population's standard deviation, not the mean, sum, or median.