Statistics Symbol Matching: Sample vs. Population Parameters

This question requires matching symbols used for sample statistics with their corresponding symbols for population parameters.

Symbol Match Explanation

We examine the standard statistical notation to determine the correct pairings:

Covariance Match: Sample ($S_{xy}$) vs Population ($\sigma_{xy}$)

• The symbol $S_{xy}$ in List I denotes the sample covariance, which measures the variance of two variables in a sample.
• The symbol $\sigma_{xy}$ in List II denotes the population covariance, measuring the same relationship across the entire population.
• Therefore, the correct match is B-IV ($S_{xy}$ to $\sigma_{xy}$).

Variance Match: Sample ($S^2$) vs Population ($\sigma^2$)

• The symbol $S^2$ in List I represents the sample variance, measuring data dispersion within a sample.
• The symbol $\sigma^2$ in List II represents the population variance, the corresponding measure for the entire population.
• Thus, the correct match is C-I ($S^2$ to $\sigma^2$).

Correlation Match: Sample ($r_{xy}$) vs Population ($\rho_{xy}$)

• The symbol $r_{xy}$ in List I stands for the sample correlation coefficient, indicating the strength and direction of a linear relationship in a sample.
• The symbol $\rho_{xy}$ in List II stands for the population correlation coefficient, representing the same relationship in the population.
• This leads to the correct match D-II ($r_{xy}$ to $\rho_{xy}$).

Mean Symbol Association: $\mu$ vs $\bar{x}$

• List I presents $\mu$ (typically the population mean) under the category 'Sample Statistics'.
• List II presents $\bar{x}$ (the sample mean) under the category 'Population Parameter'.
• The provided correct answer pairs A with III ($\mu$ with $\bar{x}$). While standard notation designates $\mu$ as the population parameter and $\bar{x}$ as the sample statistic, this pairing likely connects the concepts of mean estimation, where $\bar{x}$ is the statistic estimating $\mu$. This highlights a potential inconsistency in the question's setup but clarifies the intended association.

Considering the accurate pairings for covariance, variance, and correlation, along with the conceptual association for the mean, the complete correct matching is A-III, B-IV, C-I, D-II.