Answer :
Final answer:
The questions involve the use of hypothesis testing and the interpretation of percentiles in a statistical context, specifically focusing on the subjects of study times among students and how these compare to a known average or claim.
Explanation:
The question refers to the statistics concept of hypothesis testing, where the goal is to determine whether a statistical claim about a population parameter is supported or refuted by a sample drawn from the population. Specifically, it touches upon determining whether the average number of hours college freshman students study per day matches the academic group's claim using a sample mean and standard deviation.To test the claim, a one-sample t-test could be used, as the sample size is small, and we operate under the assumption that the population standard deviation is unknown. This test compares the sample mean to a known population mean to determine if there are statistically significant differences between them. For the case where we are testing national averages against sample means, the t-distribution is appropriate due to the sample size and the unknown population standard deviation.Furthermore, percentiles provide information about the distribution of study hours among students, with reference to whether a certain study time is high or low without any value judgment. For example, stating that the 30th percentile of study hours is seven means that 30 percent of students study seven hours or less per week.
