Problem 6. Two - way ANOVA, completely randomized design (10 points) The data that follow are the ratings for six smart phones from each of four suppliers, three of which cost $650 or more and three of which cost less than $650. The ratings have a maximum value of 100 and a minimum of 0. Supplier A B C D Cost $650 or more 76 74 72 75 LargeCost 74 69 71 73 69 68 71 73 Less than$ 650 69 69 71 72 Small Cost 67 64 71 71 64 60 70 70 a. What type of experiment was used to obtain the ratings for smartphones? What are factors? What are the levels of each factor? b. Produce an analysis of variance table appropriate for this design using R. c. Is there significant interaction between the two factors? d. Is there a main effect due to suppliers? e. Is there a main effect due to cost? For c- e, test appropriate hypothesis using o = 0.05 For this problem you have to present . the answers for question a. . the code required to obtain ANOVA table and analysis of variance table (R output) . conclusion about the truth of null hypothesis of no interaction between the factors . conclusion about the truth or falsity of null hypothesis about the equality of population means for two different types of costs and null hypothesis of equality of population means for rating of four different suppliers. . the code required to obtain the results of Tukey's comparisons . the result of Tukey's comparisons (R output) for the ratings of four different suppliers. . the diagram for population means of ratings for 4 supliers (A, B, C, and D). To draw the diagram, you have to find all sample means (mean ratings for 4 suppliers) and place the sample means in ascending order. Place the population means muA, muB, muc, and muD in the same order. Use p -values obtained as the result of Tukey's HSD test to decide which population means may be considered as not significantly different. Underline these population means on the diagram