This project computes the two largest eigenvalues of a 50x50 matrix. You will use the usual Power Method to compute the largest eigenvalue. For the next largest eigenvalue, you can use an “Annihilation or Deflation or Shifting technique” discussed in class and also in our book. The matrix A is tridiagonal. Its main diagonal has ones on it. The super diagonal (the diagonal above the main diagonal) has negative-ones on it. The sub-diagonal (below the main diagonal) has negative-ones also. Our starting vector xo has all ones. Our tolerance is 0.01.Turn in the following on one page1) Draw Gershgorin Circles that contain the eigenvalues of A. Use “insert” from the menu to locate and draw circles. 2) Based on part (1), what is the spectral radius of A. Print your answer here: _______________3) With a starting vector xo= [1 1 1 1….1]T, apply the usual power method to estimate lmax , the dominant- eigenvalue of matrix A. Use a tolerance of 0.01. Print your answer with 4 decimals: ____________4) Print the number of iterations required to converge. ____________5) Use the deflation technique discussed in class to compute the second largest eigenvalue. Tolerance = 0.01 Print the second largest eigenvalue with 4 decimals: _________________6) Print the number of iterations required to converge. ___________7) Print your computer program here. As discussed in class, the main body of your program is 3 lines, so your program should not be long.

Question 1 2 ptsMonika wants to measure the amount of money that different graduate school students spend on fast food (measured in dollars). She selects 20 random graduate students at CSUN, 20 random graduate students at UCLA, and 20 random graduate students from USC. She then measures the total amount of money each student spends on fast food at the end of one week. She wants to see (overall) if the amount of money spent by students is significantly different across the different schools. Which type of analysis is appropriate to test for this?Group of answer choicesFactorial ANOVAOne-way ANOVATukey HSD testScheffe adjustmentQuestion 2 2 ptsJohn conducts a one-way ANOVA to compare 4 different groups (using an a = 0.05) and finds that they are significantly different from each other. He is interested in seeing which groups are significantly different from each other, so he conducts a Tukey HSD post-hoc test afterwards (using a = 0.05). However, he wants to make sure that his total Type I error for the one-way ANOVA and the post-hoc test is only 5% (not 10%). Using a Bonferroni adjustment, what would his new alpha level be?Group of answer choices0.010.01250.0250.017Question 3 2 ptsYou design a study to be a 2 x 3 Factorial ANOVA. Choose the correct amount of independent variables and levels in each independent variableGroup of answer choices2 independent variables, 6 levels in the 1st independent variable, 6 levels in the 2nd independent variable3 independent variables, 2 levels in the 1st independent variable, 2 levels in the 2nd independent variable2 independent variables, 2 levels in the 1st independent variable, 3 levels in the 2nd independent variable3 independent variables, 3 levels in the 1st independent variable, 3 levels in the 2nd independent variableQuestion 4 2 ptsIn a one-way ANOVA, the Within Groups Error we calculate is based on the difference of each individual's DV score from their group's mean. Group of answer choicesTrueFalseQuestion 5 2 ptsWhen you only have two different categorical groups in your IV, performing a dependent samples t-test and a one-way ANOVA will result in the exact same p-value.Group of answer choicesTrueFalseQuestion 6 4 ptsYou run four different one-way ANOVAs. You would like to reduce your Type I error (because after these 4 tests, your Type I error chance is ~20%)! Based on the number of tests you ran, you determine that you need to lower your alpha level to 0.0125 for each ANOVA. If each ANOVA has 3 groups in it (a = 3) and each group has 16 participants (s = 16), what is your new critical F value with this lower alpha level?(Round your answer to two decimal places)Question 7 4 ptsAfter conducting a one-way ANOVA, you find that there are significant differences across four different groups. Each group has an equal number of people in it, so you decide to follow this one-way ANOVA with a Scheffe adjustment to see which of these groups are significantly different from each other. You calculate the final Scheffe value to be 3.256. Based on the means of each group (below), identify ALL of the following groups that are significantly different from each other...Group 1: 5.248 Group 2: 7.589 Group 3: 8.562 Group 4: 3.123Group of answer choicesGroup 2 vs. Group 4 Group 3 vs. Group 4Group 1 vs. Group 3 Group 2 vs. Group 4 Group 3 vs. Group 4Group 1 vs. Group 2 Group 2 vs. Group 3 Group 1 vs. Group 4Group 1 vs. Group 3Group 2 vs. Group 3Question 8 2 ptsTo do a 2x2 factorial ANOVA by hand, you need to have way too much time on your hands, a lot of formulas written down, and a lot of practice (especially for exam 3). (Choose answer "Yes" below -- it is the correct answer)Group of answer choicesNoMaybeYesI don't know!Question 9 6 ptsGiven the data for a one-way ANOVA (below), calculate the Sums of Squares Between Groups. Round your answer to two decimal points. ParticipantGroup 1Group 2Group 3S120 22 18 S212 20 40 S316 19 10 S416 24 20 (Hint: start by finding the means for the groups...)Question 10 4 ptsThe following Summary Table is incomplete. For this one-way ANOVA, find the missing F value. Source Sums of Squares Degrees of Freedom Mean Square F Between Groups 420 2 Within Groups Total 1764 23 Group of answer choices2104.310.302.733.28Question 11 4 ptsGiven the following summary table for a one-way ANOVA, calculate an Omega Squared effect size estimate:Source Sums of Squares Degrees of Freedom Mean Square F Between Groups 12.56 4 3.14 1.584Within Groups 188.29 95 1.982 Total 200.85 99 Group of answer choices0.08220.04510.03550.0228Question 12 2 ptsIf you have a Factorial ANOVA design with two independent variables, you must test to see if your first IV is significant, if your 2nd IV is significant, and whether an interaction of the two IV's is significant. Group of answer choicesTrueFalseQuestion 13 2 ptsWhich of the following is an example of a simple effect analysis in a Factorial ANOVA?Group of answer choicesThere are significant differences across all groups of the 1st IV.There are significant differences across all levels of the 1st IV, but only for one level of the 2nd IV,There are significant differences across all combinations of groups from both IV1 and IV2.In the 1st IV, group 1 is significantly different than group 2, but group 1 is not significantly different than group 3.Question 14 4 ptsCalculate a Tukey HSD value for a one-way ANOVA (based on the following information)...qT = 4.201 MS (within) = 21.88 n = 15Group of answer choices6.1286.86576.115.5355.07Question 15 2 ptsGiven the following group means from a 2 x 2 Factorial ANOVA: Variable A Group 1 Group 2 Variable B Group 1 20 40Group 2 20 40Which variables (if any) show a main effect?Group of answer choicesThere is a main effect of both Variable A and Variable B.There is no main effect for either Variable A or Variable B.There is a main effect of Variable B only.There is a main effect of Variable A only.Question 16 2 ptsIf you have designed a research study with 1 categorical IV (which is split into three separate groups) and 1 ratio DV, you should use a one-way ANOVA to determine if there are any significant differences across all of the groups. Group of answer choicesTrueFalseQuestion 17 2 ptsIn a one-way ANOVA, the three main factors that influence Within Group error are:1. How close the group means are to each other2. How spread out the variances of the groups are3. Whether your IV is a categorical vs. ordinal variableGroup of answer choicesTrueFalseQuestion 18 2 ptsPost-hoc tests are conducted ...Group of answer choicesAfter a one-way ANOVA, to see if the overall one-way ANOVA was significant or not.After a one-way ANOVA, to see which groups are significantly different from each other.Before a one-way ANOVA is conducted, to see which groups are significantly different from each other firstWhen we want to see how influential the IV is in changing the DV.

Case Study: Statistical Inference Overview The research department of an appliance manufacturing firm has developed a solid-state switch for its blender that the research department claims will reduce appliance returns under the one-year full warranty by 3%–6%. To determine if the claim can be supported, the testing department selects a group of the blenders manufactured with the new switch and a group with the old switch and subjects them to a normal year’s worth of wear. Out of 250 blenders tested with the new switch, nine would have been returned. Sixteen would have been returned out of the 250 blenders with the old switch. As the manager of the appliance manufacturing process, use a statistical procedure to verify or refute the research department’s claim.