A professor who teaches a large introductory statistics class (197 students) with eight discussion sections would like to test if student performance diers by discussion section, where each discussion section has a dierent teaching assistant. The summary table below shows the average final exam score for each discussion section as well as the standard deviation of scores and the number of students in each section. Sec 1 Sec 2 Sec 3 Sec 4 Sec 5 Sec 6 Sec 7 Sec 8 ni 33 19 10 29 33 10 32 31 xi 92.94 91.11 91.80 92.45 89.30 88.30 90.12 93.35 si 4.21 5.58 3.43 5.92 9.32 7.27 6.93 4.57 The ANOVA output below can be used to test for dierences between the average scores from the dierent discussion sections. Df Sum Sq Mean Sq F value Pr(>F) section 7 525.01 75.00 1.87 0.0767 Residuals 189 7584.11 40.13 Conduct a hypothesis test to determine if these data provide convincing evidence that the average score varies across some (or all) groups. Check conditions and describe any assumptions you must make to proceed with the test.

Q: A professor who teaches a large introductory statistics class (197 students) with eight discussionsections would like to test if student performance differs by discussion section, where eachdiscussion section has a different teaching assistant. The summary table below shows the averagefinal exam score for each discussion section as well as the standard deviation of scores and thenumber of students in each section.The ANOVA output below can be used to test for differences between the average scores from thedifferent discussion sections.Conduct a hypothesis test to determine if these data provide convincing evidence that the averagescore varies across some (or all) groups. Check conditions and describe any assumptions you mustmake to proceed with the test. Step By Step Solution:Step 1 of 3:Checking the conditions:Independent: It is assumed that the students are independent in each different section.Normal: As shown in the table, many groups have students less than 30, thus normally distributed.Equal variances: The ratio of largest and smallest SD is less than 4.