Question
Quiz Active TIME REMAINING Zachary completes a hypothesis test and finds that he rejects the null hypothesis. Which statement gives a reason for rejecting the null hypothesis? The \( z \)-statistic is less than 0 . The \( z \)-statistic lies in the critical region. The \( z \)-statistic lies outside the critical region. The \( z \)-statistic is greater than 0 .
Ask by Whittaker Romero. in the United States
Feb 25,2025
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Answer
The null hypothesis is rejected because the z-statistic lies in the critical region.
Solution
The reason for rejecting the null hypothesis is that the z-statistic lies in the critical region. This indicates that the test statistic has reached an extreme value relative to the hypothesized distribution under the null hypothesis, leading to its rejection.
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Zachary rejects the null hypothesis because the \( z \)-statistic lies in the critical region. This critical region is determined by the significance level chosen for the test (like 0.05), and if the \( z \)-statistic exceeds this boundary, it suggests strong enough evidence against the null hypothesis. In hypothesis testing, rejecting the null hypothesis typically indicates that the results observed are statistically significant. This leads to the conclusion that the alternative hypothesis may be true, and it opens the door for further exploration or action based on these findings.
