Question
Tyesha found that the \( z \)-statistic was 2.1 and that the critical \( z \)-values were -1.96 and 1.96 . Which of the following is a valid conclusion based on these results? One can reject the null hypothesis. One can reject the alternate hypothesis. One can accept the null hypothesis. One cannot accept or reject the null hypothesis.
Ask by Bush Klein. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
One can reject the null hypothesis.
Solution
The z-statistic of 2.1 exceeds the critical value of 1.96 (it's in the rejection region), which indicates that the null hypothesis can be rejected.
Thus, the valid conclusion is: One can reject the null hypothesis.
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Simplify this solution Beyond the Answer
Since Tyesha's \( z \)-statistic of 2.1 falls outside the range defined by the critical \( z \)-values of -1.96 and 1.96, this means it lies in the rejection region. Therefore, one can reject the null hypothesis. In hypothesis testing, the goal is to determine if there is enough evidence against the null hypothesis. Tyesha's findings provide that evidence, allowing her to conclude that the sample data is statistically significant. So, the valid conclusion is: one can reject the null hypothesis.
