What does a T-statistic measure?

A T-statistic is a standardized value that indicates how many standard deviations a sample mean is from the population mean, or how far it is from a hypothesized value. It plays a crucial role in hypothesis testing, allowing analysts to determine if the observed data significantly deviates from what was expected under the null hypothesis. When calculating the T-statistic, the sample mean is subtracted from the hypothesized value, and this difference is divided by the standard error of the sample mean. This quantifies the distance of the sample observation from the hypothesized value in units of standard error, which is essential for determining significance in statistical tests.

The other choices involve different concepts: while the first option discusses the deviation of a sample statistic from the population mean, it does not fully capture the standardized context that the T-statistic represents. The second option relates to regression analysis, focusing specifically on the coefficients rather than on the sample's distance from a hypothesized value. The last choice pertains to calculating an average return, which is not a function of the T-statistic but rather an expression of central tendency. Therefore, the choice that accurately defines the scope and utility of the T-statistic in statistical analysis is the measurement of how far an observed sample statistic is from