Q3 [11 pts] One-way ANOVA Analysis. A researcher is interested in comparing the effectiveness of three different teaching methods on students' test scores. The students are randomly assigned to one of the three groups: Group A (Lecture), Group B(Interactive), and Group C(online). After a month of instruction, each student takes the same standardized test, and the scores are recorded. The data are as follows: Group A B C Data Sample size 82,85,79,88,84 5 90,92,95,89,93 78,81,80,77,76 5 5 x S 83.6 3.36 91.8 2.39 78.4 2.07 The overall mean (a.k.a. grant mean) = ((83.6)(5)+91.8(5)+78.4(5))/(5+5+5)= 84.6 (a) [1 pt] What does ANOVA stand for? (b) [1 pt] Check the standard deviation condition for ANOVA, can we safely proceed with the ANOVA analysis? (c) [2 pts] What are the null and alternative Hypotheses for this one-way ANOVA test? (d) [4 pts] Calculate the sum of squares between groups (SSG) and the MSG, also calculate the sum of squares within group (SSE) and the SSE. Round your results up to 4 decimal places. (e) [1 pt] Determine the F statistic value. Round your results up to 4 decimal places. (f) [2pt] Use the Finding probability Shiny app (choose F distribution) to determine the p-value for this ANOVA test? What conclusion do you have at 5% significance level?