Final answer:
The question is about comparing a test statistic to a critical z-value in a hypothesis test. With a test statistic of 3.88 and a critical z-value of ± 1.96, the null hypothesis should be rejected as the test statistic exceeds the critical value.
Step-by-step explanation:
The subject of this question is a hypothesis test in the field of Mathematics, more specifically the topic of statistics at the college level. In this scenario, a student is given a test statistic of 3.88 and is required to compare this to a critical z-value of ± 1.96 for a two-tailed hypothesis test.
If the test statistic falls outside the range of the critical values, it suggests that the null hypothesis should be rejected. The critical region starts at a z-score of ± 1.96, which corresponds to a 95% confidence level (since each tail has an area of 0.025), for a total area of 0.05 in the critical region. Given that a test statistic of 3.88 exceeds the positive critical value of 1.96, the null hypothesis would be rejected because the test statistic lies in the critical region.