Question

The ​t-statistic is calculated by​ dividing: A. the slope by the standard deviation of the explanatory variable. B. the estimator minus its hypothesized value by the standard error of the estimator. C. the slope by 1.96. D. the OLS estimator by its standard error.

Answer 1

The t-statistic is calculated by dividing the estimator minus its hypothesized value by the standard error of the estimator, which is a key component in hypothesis testing when the population standard deviation is unknown.

(Option B)

Step-by-step explanation:

The question asks how the t-statistic is calculated. The correct calculation of the t-statistic is by dividing the estimator minus its hypothesized value by the standard error of the estimator. This process is used when conducting hypothesis tests where the population standard deviation is unknown and the sample standard deviation is used as an estimate.

The standard error is crucial in this calculation, which quantifies the amount by which an estimate from the data is likely to differ from the true population value because of chance variation when drawing random samples. This method employs the sample standard deviation as an estimate and emphasizes the significance of the standard error in gauging the likelihood of chance variation in estimates drawn from random samples.

Answer 2

B. the estimator minus its hypothesized value by the standard error of the estimator.

Step-by-step explanation:

In the T-test, the T-Statistic is used to decide whether you should support or reject the null hypothesis. It is similar to the z-statistic. It is used when we have a small sample size.

In the case of small sample statistics, the t-statistic is calculated which replaces the z-statistics.

T-statistic is calculated as follow

T-Statistics = ( Estimator - Hypothesized value of the estimator ) / Standard error of the estimator