A college professor would like to estimate the proportion of students who pull an "all-nighter,” meaning they study all night for an upcoming exam. She selects a random sample of 100 students from her large college and finds that the 99% confidence interval for the true proportion of students who pull an all-nighter is 0.48 to 0.62. Which of these statements is a correct interpretation of the confidence level? A) Approximately 99% of all students have pulled an all-nighter.
B) There is a 99% probability that the true proportion of all students who pull an all-nighter is between 0.48 and 0.62.
C) If many random samples of size 100 are selected from all students at this college, approximately 99% of the intervals would capture the true proportion who pull an all-nighter.
D) Approximately 99% of the sample proportions of students who pull an all-nighter, based on random samples of size 100 from the population of all students at this college, will fall between 0.48 and 0.62.