\( H_{0}: \mu_{a}-\mu_{b}=0 \) \( H_{a}: \mu_{a}-\mu_{b}>0 \) In a large sample, \( \bar{x}_{a}-\bar{x}_{b}=3.376 \) with a standard error of 2.034 Compute the test statistic using the general formula for a test statistic: test statistic \( =\frac{\text { sample statistic-null parameter }}{\text { standard error }} \) Round your final answer to three decimal places.

To compute the test statistic using the given formula, we plug in the values: 1. Sample statistic: \( \bar{x}_{a} - \bar{x}_{b} = 3.376 \) 2. Null parameter: \( \mu_{a} - \mu_{b} = 0 \) 3. Standard error: \( SE = 2.034 \) Now, using the formula for the test statistic: \[ \text{test statistic} = \frac{\bar{x}_{a} - \bar{x}_{b} - (\mu_{a} - \mu_{b})}{SE} \] Substituting the values: \[ \text{test statistic} = \frac{3.376 - 0}{2.034} = \frac{3.376}{2.034} \approx 1.661 \] Rounding to three decimal places, the test statistic is approximately **1.661**.