A test of \( H_{0}: \mu=51 \) versus \( H_{1}: \mu \neq 51 \) is performed using a significance level of \( \alpha=0.05 \). The value of the test statistic is \( z=1.97 \). Part: \( 0 / 3 \) Part 1 of 3 Determine whether to reject \( H_{0} \). Since the test statistic \( \square \) is in the critical region, we \( \square \) reject \( H_{0} \) at the \( \alpha=0.05 \) level. \( \square \)

To determine whether to reject \( H_{0} \), we first need to find the critical z-values for a two-tailed test at the \( \alpha=0.05 \) significance level. The critical z-values are approximately \( -1.96 \) and \( 1.96 \). Since the calculated test statistic \( z = 1.97 \) falls just outside the lower critical value but just into the upper critical region, we can conclude that we are in the critical region. Since the test statistic \( 1.97 \) is in the critical region, we reject \( H_{0} \) at the \( \alpha=0.05 \) level. So, the filled statement would be: Since the test statistic \( 1.97 \) is in the critical region, we reject \( H_{0} \) at the \( \alpha=0.05 \) level.