Which statement regarding the denominator of the equation for the z score and that of the z statistic is true?
A) There is no difference between the denominators of the two equations.In both cases, we divide by the standard error.
B) There is no difference between the denominators of the two equations.In both cases, we divide by the standard deviation.
C) When computing a z score, we divide by the population standard deviation, but when computing a z statistic, we divide by the standard error of the sampling distribution.
D) When computing a z statistic, we divide by the population standard deviation, but when computing a z score, we divide by the standard error of the sampling distribution.

Question

Quizplus · Accepted Answer

When computing a z score, we are comparing an individual score to the population mean using the population standard deviation. Therefore, we divide the difference between the individual score and the mean by the population standard deviation. 
However, when computing a z statistic, we are comparing a sample mean to the population mean. In this case, we divide the difference between the sample mean and the population mean by the standard error of the sampling distribution, which takes into account the variability of sample means. The denominator of the z statistic equation is thus different from that of the z score equation.

Which Statement Regarding the Denominator of the Equation for the Z