Calculating a One-Sample Z-Test Statistic

In hypothesis testing, a test statistic is a standardized value that is calculated from sample data during a hypothesis test. It measures the size of the difference relative to the variation in the sample data. In a one-sample z-test, the test statistic is computed using the formula:

$$ z = \f\frac{\bar{x} - \mu_0}{\f\frac{\sigma}{\sqrt{n}}} $$

Where:

• $$ \bar{x} $$ = sample mean
• $$ \mu_0 $$ = population mean under the null hypothesis
• $$ \sigma $$ = population standard deviation
• $$ n $$ = sample size

Given a sample mean of 50, a population mean under the null hypothesis of 48, a population standard deviation of 12, and a sample size of 36, what is the value of the test statistic?