Final answer:
A hypothesis test, specifically a one-sample t-test, is required to determine if the mean study time of freshman students is at least 2.5 hours per day based on a sample of 30 students with a mean of 137 minutes and standard deviation of 45 minutes.
Step-by-step explanation:
The question relates to a statistical hypothesis test where we analyze whether the mean study time of freshman students is at least 2.5 hours per day. A class conducted a random sample analysis of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At an alpha (α) level of 0.01, we need to perform a hypothesis test to see if this sample evidence supports the student academic group's claim that freshmen study at least 2.5 hours (150 minutes) per day, on average.
To answer whether the claim is correct, we perform a one-sample t-test (since the sample size is less than 30) with the null hypothesis being that the average study time is at least 150 minutes. The alternative hypothesis would be that the average study time is less than 150 minutes. Critical values or a p-value would be calculated using the mean, standard deviation, and sample size to determine whether to accept or reject the null hypothesis.