Student performance across discussion sections: A professor who teaches a large introductory statisticsclass (197 students) with eight discussion sections would like to test if student performance differs bydiscussion section, where each discussion section has a different teaching assistant. The summary table belowshows the average final exam score for each discussion section as well as the standard deviationthe number of students in each section.Scores andSec 1Sec 2Sec 3Sec 4Sec 5Sec 6Sec 7Sec 8ni3319102933323192.9491.1191.892.4589.388.390.1293.45Si4.215.583.435.929.327.276.934.57The ANOVA output below can be used to test for differences between the average scores from the differentdiscussion sections.dfSum SqMean SqF valuePr(F)section525.01751.870.0767residuals1897584.1140.13Conduct a hypothesis test to determine if these data provide convincing evidence that the average scorevaries across some (or all) groups. Check conditions and describe any assumptions you must make to proceedwith the test.(a) Write the hypotheses for evaluating if there is a difference between average scores across sections in yourown words.Ho: µ1 = P2 = ... = P8Ha: At least one pair of means is differentO Ho: H1 = H2 =Ha: At least one pair of means is the same= P8...Ho: µ1 = P2 = ...= H8%3DHa: µ1 z P2 ² ...(b) Assume that the conditions required for this inference are satisfied.(c) What is the test statistic associated with this ANOVA test?(please round to two decimal places)(d) What is the p-value associated with this ANOVA test?(please round to four decimal places)(e) Interpret the conclusion of the test in the context of the study:O Since p 2 0.05, there is no difference in average scores across the different sectionsO Since p is close to 0.05, we cannot make a decisionOSince p 2 0.05, there is enough evidence to claim a difference in average scores across the differentsections Conduct a hypothesis test to determine if these data provide convincing evidence that the average scorevaries across some (or all) groups. Check conditions and describe any assumptions you must make to proceedwith the test.(a) Write the hypotheses for evaluating if there is a difference between average scores across sections in yourown words.O Ho: H1 = H2 =%3D=...Ha: At least one pair of means is differentHo: µ1 = P2 = ... = P8Ha: At least one pair of means is the sameHo: µ1 = P2 = ... = P8Ha: µ1 * P2 * ... ± µ8(b) Assume that the conditions required for this inference are satisfied.(c) What is the test statistic associated with this ANOVA test?(please round to two decimal places)(d) What is the p-value associated with this ANOVA test?(please round to four decimal places)(e) Interpret the conclusion of the test in the context of the study:OSince p 2 0.05, there is no difference in average scores across the different sectionsSince p is close to 0.05, we cannot make a decisionOSince p 2 0.05, there is enough evidence to claim a difference in average scores across the differentsectionsO Since p 2 0.05, we do not have enough evidence to claim a difference in average scores across thedifferent sectionsSubmit All PartsO O

Question

Student performance across discussion sections: A professor who teaches a large introductory statisticsclass (197 students) with eight discussion sections would like to test if student performance differs bydiscussion section, where each discussion section has a different teaching assistant. The summary table belowshows the average final exam score for each discussion section as well as the standard deviationthe number of students in each section.Scores andSec 1Sec 2Sec 3Sec 4Sec 5Sec 6Sec 7Sec 8ni3319102933323192.9491.1191.892.4589.388.390.1293.45Si4.215.583.435.929.327.276.934.57The ANOVA output below can be used to test for differences between the average scores from the differentdiscussion sections.dfSum SqMean SqF valuePr(>F)section525.01751.870.0767residuals1897584.1140.13Conduct a hypothesis test to determine if these data provide convincing evidence that the average scorevaries across some (or all) groups. Check conditions and describe any assumptions you must make to proceedwith the test.(a) Write the hypotheses for evaluating if there is a difference between average scores across sections in yourown words.Ho: µ1 = P2 = ... = P8Ha: At least one pair of means is differentO Ho: H1 = H2 =Ha: At least one pair of means is the same= P8...Ho: µ1 = P2 = ...= H8%3DHa: µ1 z P2 ² ...(b) Assume that the conditions required for this inference are satisfied.(c) What is the test statistic associated with this ANOVA test?(please round to two decimal places)(d) What is the p-value associated with this ANOVA test?(please round to four decimal places)(e) Interpret the conclusion of the test in the context of the study:O Since p 2 0.05, there is no difference in average scores across the different sectionsO Since p is close to 0.05, we cannot make a decisionOSince p 2 0.05, there is enough evidence to claim a difference in average scores across the differentsections Conduct a hypothesis test to determine if these data provide convincing evidence that the average scorevaries across some (or all) groups. Check conditions and describe any assumptions you must make to proceedwith the test.(a) Write the hypotheses for evaluating if there is a difference between average scores across sections in yourown words.O Ho: H1 = H2 =%3D=...Ha: At least one pair of means is differentHo: µ1 = P2 = ... = P8Ha: At least one pair of means is the sameHo: µ1 = P2 = ... = P8Ha: µ1 * P2 * ... ± µ8(b) Assume that the conditions required for this inference are satisfied.(c) What is the test statistic associated with this ANOVA test?(please round to two decimal places)(d) What is the p-value associated with this ANOVA test?(please round to four decimal places)(e) Interpret the conclusion of the test in the context of the study:OSince p 2 0.05, there is no difference in average scores across the different sectionsSince p is close to 0.05, we cannot make a decisionOSince p 2 0.05, there is enough evidence to claim a difference in average scores across the differentsectionsO Since p 2 0.05, we do not have enough evidence to claim a difference in average scores across thedifferent sectionsSubmit All PartsO O

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The ANOVA output below can be used to test for differences between the average scores from the…