Confidence Intervals (16 points/8 each) 6. I am interested in determining if exam scores significantly differ between students in online classes and students in face-to-face classes. Before COVID (pre-2020), I taught Plants and Humans, a freshman- level biology course, for seven semesters with face-to-face delivery. The population mean for Exam 1 for N = 84 students over those seven semesters was = 75.4 with a population standard deviation of = 19.6. After 2020, I began delivering the course online. In spring semester 2021, I had n = 17 students, and the sample mean for Exam 1 was x = 84.9 with a sample standard deviation of s= 16.8. a) Determine a 99%CI for mean Exam 1 score for the 2021 online class and assume a population SD () of 19.6 (the same as pre-2020 classes). b) Determine a 90%CI for mean Exam 1 score for the 2021 online class without assuming you have a population SD available (use sample SD, s). Bonus: Based on this data, are mean Exam 1 scores for online and face-to-face classes statistically the same (does for pre-2020 classes fall within either of the CI's)? (4 bonus points) n z x 2 /n s t x2 /

Hypothesis Testing (16 points/8 each) 7. We will now directly test the hypothesis that Exam 1 scores significantly differ between students in online classes and students in face-to-face classes. z-test a) Using a confidence level of 99%and the population SD ()of pre-2020 classes, are we very confident that mean Exam 1 scores for students in online classes are the same as for students in face-to-face classes (Reject or Do not reject)? t-test b) Using a confidence level of 90%and the sample population SD (s) of the spring 2021 class, are we very confident that mean Exam 1 scores for students in online classes are the same as for students in face-to- face classes (Reject or Do not reject)?