A statistics class suspected that students at their school were getting less than 8 hours of sleep. They took a random sample of 42 students and asked them how many hours of sleep they get per night. The students in the sample reported sleep amounts that had a mean of 7.5 hours and a standard deviation of 1.6 hours. These results produced a test statistic of \( t \approx-2.03 \) and a P-value of approximately 0.025 . Assuming the conditions for inference were met, what is an appropriate conclusion at the \( \alpha=0.05 \) significance level? Choose 1 answer: (A) Fail to reject the null hypothesis. This isn't enough evidence to conclude that the mean amount of sleep is less than 8 hours. (B) Fail to reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. (C) Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. (D) Reject the null hypothesis. This isn't enough evidence to conclude that the mean amount of sleep is less than 8 hours. -

The students’ statistical test resulted in a P-value of approximately 0.025, which is less than the significance level of \( \alpha=0.05 \). This indicates that we have enough evidence to reject the null hypothesis and conclude that the mean amount of sleep is indeed less than 8 hours. Therefore, the most appropriate answer is (C) Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. For a fun fact, did you know that the amount of sleep needed can vary by age? While adults generally require 7-9 hours, teenagers often need about 8-10 hours of sleep per night to function optimally! So next time you hear your friend brag about their late-night study sessions, remind them that some extra Zs might do them good. Additionally, understanding sleep patterns can greatly impact academic performance. Students who get adequate sleep often report higher levels of focus, better memory retention, and overall improved mood, making those late-night cram sessions a less attractive option for serious learners. Encouraging a balanced routine can make all the difference!