HP340: Statistical Methods, Spring 2015Due: 3:30 p.m., Tuesday Mar 31, 2015Homework 8Total Points: 50Show your work/explain your reasoning when calculations are required. Late assignments will notbe accepted. 1. (8 points total) a. (2 points) In a one-factor between-subjects analysis of variance, the F statistic is defined as ________.a. MSA / dfError b. MSTotal / MSErrorc. SSA / dfA d. MSA / MSErrore. SSError / dfError b. (2 points) SSA and SSError are also called ___________ and ____________ sums of squares, respectively.a. between groups; mean groupsb. within groups; between groupsc. between groups; within groupsd. treatments; within groupse. c and dc. (2 points) If SStotal = 80, SSA = 50, SSError = 30, dftotal = 15, dfA = 3, and dfError = 12 in a one-factor between-subjects analysis of variance, then MSError =_____a. 1.43b. 0.83c. 2.5d. 16.67e. 5.33d. (2 points, show your work) Based on the sums of squares and degrees of freedom above in (c), what are the values of Fobs and Fcrit (assume α=0.05)?a. 2.13; 3.29b. 6.67; 3.29c. 2.13; 3.49d. 6.67; 3.49e. a or c2. (30 points, total) The napping times of 5 preschool, kindergarten, and 1st grade students are shown in the table below (in minutes).Preschool Kindergarten 1st Grade30 15 1520 19 1225 17 1322 17 1523 20 17a. (2 points) State the null and alternative hypotheses when investigating difference in the napping times between in the three levels of schooling.b. (15 points) Showing all of your work, construct an ANOVA table and find FobsSS df MSBetween GroupsWithin GroupsTotalc. (3 points) What is your decision regarding the hypotheses stated in a. for α=0.01?d. (5 points) Perform the ANOVA using JMP (include the JMP output in your homework excluding graphs)e. (5 points) Calculate the Tukey CD and interpret the pairwise comparisons.3. (12 points total) a. (8 points, show your work) Fill in the missing cells (denoted with ?) in the following ANOVA table:SS df MS FBetween Groups 100 ？ ? ?Within Groups ？ 25 ?Total 235 29 b. (4 points) For the completed table above:I. How many levels of factor A are there? II. How many subjects are there for each group? III. What is the total number of subjects in the study? IV. Is Fobs significant for