Rejection Point (Critical Value) for the Test Statistic

A rejection point (critical value) for a test statistic is a value with which the computed test statistic is compared to decide whether to reject or not reject the null hypothesis.

[Practice Problems] An investment consultant conducts two independent random samples of 5-year performance data for US and European absolute return hedge funds. The consultant decides to test whether the two means are statistically different from one another at a 0.05 level of significance. The two populations are assumed to be normally distributed with unknown but equal variances.

[Solutions] A

The t-statistic value of 0.4893 does not fall into the critical value rejection regions (≤ –1.984 or > 1.984). Instead it falls well within the acceptance region. Thus, H₀ cannot be rejected; the result is not statistically significant at the 0.05 level.