Question

cameron wondered if the average score on a final exam was different between those who texted on a regular basis during lecture for a particular class and those that did not text at all during lecture for the same class. which of the following is the correct statement of what a type ii error is in the context of this problem?
choose the correct answer below.
○ a. cameron did not have evidence that there was a difference in the average scores on the final exam between those who texted during lecture and those who did not text during lecture, and there really was no difference in the average scores.
○ b. cameron had evidence that there was a difference in the average scores on the final exam between those who texted during lecture and those who did not text during lecture when there was no difference in the average scores.
○ c. cameron had evidence that there was a difference in the average scores on the final exam between those who texted during lecture and those who did not text during lecture, and there really was a difference in the average scores.
○ d. cameron did not have evidence that there was a difference in the average scores on the final exam between those who texted during lecture and those who did not text during lecture when there was a difference in the average scores.

Explanation:

A Type II Error occurs when we fail to reject a false null hypothesis. In hypothesis testing, the null hypothesis (\(H_0\)) would be that there is no difference in the average scores (\(\mu_{texters}=\mu_{non - texters}\)), and the alternative hypothesis (\(H_1\)) is that there is a difference (\(\mu_{texters}
eq\mu_{non - texters}\)).

• Option A: This is a correct decision (not rejecting \(H_0\) when \(H_0\) is true).
• Option B: This is a Type I Error (rejecting \(H_0\) when \(H_0\) is true).
• Option C: This is a correct decision (rejecting \(H_0\) when \(H_1\) is true).
• Option D: Here, we do not reject \(H_0\) (no evidence of a difference) when \(H_1\) is true (there is a difference), which is the definition of a Type II Error.

Answer:

D. Cameron did not have evidence that there was a difference in the average scores on the final exam between those who texted during lecture and those who did not text during lecture when there was a difference in the average scores.