What is the purpose of using a z-statistic?

The purpose of using a z-statistic is primarily to assess the significance of differences in population means. A z-statistic is utilized in hypothesis testing, specifically when comparing the means of two populations or determining if a sample mean significantly differs from a known population mean.

In this context, the z-statistic helps quantify the distance between the sample mean and the population mean in terms of standard deviations, allowing researchers to evaluate the likelihood that an observed difference is due to random chance or is statistically significant. This plays a crucial role in decision-making based on data analysis because it provides a standardized way to interpret differences in means, especially when the population variance is known or when sample sizes are large.

While the other choices pertain to important statistical concepts, they do not accurately describe the primary function of the z-statistic as it relates to hypothesis testing and the comparison of means.