Part 3. ANDWK The General Social Survey collects data on demographics, educationr and work, among many other characteristics of US residents. Using ANDVA, we can consider educational attainment levels for all 1,1?2 respondents at once. Below are the distributions of hours worked by educational attainment and relevant summary statistics that will be helpful in carrying out this analysis. . Z$$% EH I: I Hours mm per wait a E 20 El Less than H5 Jr Col Badlalor'tl Graduate Educational attainment _Lesa than H-b H b Js'_ll HELC Halo[\"5 Era-dame Total Mean 33.6? 39.5 41.39 42.55 411.35- 4|].r15 SD [5.31 14.9? 13.1 13152 15.5] 15.17 :1 1'21 5-16 97 253 155- 1,]?'2 a. 1II'II'n'te the null and alternative hypotheses for evaluating whether the average number of hours worked varies across the five groups. b. Using the information provided assess whether the following conditions necessary to accurately perform an ANOUA F test are met. i. re the observations in the study independent? ii. Are the sample sizes sufficiently large? [Hint: the n rov.I of the table above provides the sample sizes of each group.} iii. Is the variation in the groups about equal from one group to the next?{Hint: use the spread of the boxplots and standard deviation values from the table to assess this condition.) To assess whether there is a signicant difference in the average number of hours worked between one or more of the groups, we need to determine the mean squares between groups {m and the mean squares within groups {MSEL Each of these values has an assocLatei osm- I The degrees of freedom associated with the MSTr are riff? : I 1 = 5 1 = 4- I m of freedom associated with the MSE are 5:11-21"! I 211?: 5 = 116? c. An AND'III'A was performed in FL The estimate for the mean squares between groups ism = 501.54 and the resulting F statistic is equal to 2.139. Determine the average variation within each group. That is, calculate the MSE. d. Using the Fstatistic from question 4 and the two values for the degrees of freedom in question 3, calculate the p-value for this test. e. Using the p-value calculated in question 5, write a conclusion for this ANDVA F test using a significance level oftt = 11.05. (Hint: your conclusion should include a statement of evidence in favor of the alternative and a statement as to whether the null hypothesis is rejected or not.}