Question

A random sampling of the IQ level of 100 students from Texas A&M and 100 students from Harvard results in the following two-sided confidence intervals at a 95% confidence level: Texas A&M students 130 < μ <140 Harvard students 110 < μ <120 Is it possible that the true average IQ of Harvard students is greater than the average IQ of Texas A&M students? True False QUESTION 2 An instructor of an extremely large class (1000 students) starts grading an exam. After grading 100 of the assignments he calculates the sample average as 80 with a standard deviation of 10, He then correctly determines that he can 95% confident that the average student score is between 78.04 and 81.96. He continues grading, and after grading a total of 400 exams the sample average is 80 with a sample deviation of 25. How confident is he that the average student score is still between 78.04 and 81.96? A. More than 95% confident 0% confident .95% confident (the confidence level does not change) D. Less than 95% confident

Answer 1

1)False ; as we can see that confidence interval of mean for Harvard students is lower then interval values of Texas students

2)

option D is correct ; as in second case std error of mean =25/sqrt(400)=1.25 is greater then 10/sqrt(100)=1,