Final answer:
The question does not provide enough information to determine the probability that a randomly selected student studies more than 8.74 hours per week or that the average of 89 students will study more than 8.74 hours per week. For hypothesis testing regarding student study habits, one would typically use a one-sample t-test or z-test based on the information provided about the sample and population standard deviations.
Step-by-step explanation:
The question relates to the field of statistics, specifically regarding the calculation of probabilities and the testing of hypotheses about population means based on sample statistics. When we are calculating the probability that a single student studies more than 8.74 hours per week, we would typically use the z-score formula and the normal distribution to find this probability. However, since we do not have the necessary data to compute the z-score (specifically, we need the histogram or the exact distribution of study hours), the correct answer is There is not enough information to determine.
For question (b), we would use the Central Limit Theorem to test whether the sample mean of 89 students studying more than 8.74 hours per week significantly differs from the population mean. Since we don't have a standard error for the mean of 89 students, the appropriate answer once again is There is not enough information to determine.
The scenario described in the provided information implies the use of a one-sample t-test or z-test for hypothesis testing, depending on whether the population standard deviation is known, to determine if the sample provides evidence that study habits differ from the national average or the claim made by a student group.