Question

Alex hypothesized that students study less than the recommended two hours per credit hour each week outside of class. Alex performed a hypothesis test and told a colleague that he had evidence to indicate his hypothesis was true. Which of the following is a true statement that his colleague could have​ said? 1)Alex should never accept the null hypothesis as true. 2)There was no chance Alex could have made any error. 3)Alex might have made a Type I Error. 4)Alex might have made a Type II Error.

Answer 1

The correct response to Alex's claim is that he might have made a Type I Error, which occurs when a true null hypothesis is incorrectly rejected. Alex's hypothesis testing follows the principle that hypothesis testing can't prove a hypothesis but assesses evidence against it.

Step-by-step explanation:

Among the possible responses to Alex’s claim that he has evidence to support his hypothesis, the correct statement that a colleague could say is “Alex might have made a Type I Error.” This type of error occurs when the null hypothesis is true, but is incorrectly rejected by the hypothesis test. On the other hand, a Type II Error occurs when the null hypothesis is false, but the decision is made not to reject it. Based on the provided information, Alex should never accept the null hypothesis as true, because hypothesis testing is not about proving the null hypothesis, but about assessing the evidence against it.

Since Alex found evidence to indicate his hypothesis was true and did not outright accept the null hypothesis, we can exclude the possibility of a Type II Error in this scenario. Also, there's always a chance of making an error in hypothesis testing; hence, stating there is no chance of error is incorrect.