Problem 5. One - way ANOVA, randomized block design. (2 + 3 + 4 + 3 + 3 = 15 marks) Do average automobile insurance costs differ for different insurance companies? The following are estimates (in dollars) of the cost of 6 - month polices for basic liability coverage for a person with no violations or accidents, who drives between 12,600 and 15,000 miles per year, and who lives in one of indicated areas. Location Company Riverside San Bernardino Hollywood Long Beach 1 2 3 4 21 st Century A 736 336 1492 196 Allstate B 745 725 1384 884 AAA C 668 618 1214 302 Fireman's Fund D 1065 86 1502 1571 State Farm E 1202 1172 1682 1272 a. Do the data provide sufficient sample evidence to indicate that average insurance premiums differ from a company to company? Test appropriate hypothesis at level of significance a = 0.05 using R. If there are the differences in the mean insurance premiums for different Insurance companies, indicate which means differ. Use Tukey's procedure for multiple comparisons, and draw the diagram. b. Do the data provide sufficient sample evidence to indicate that insurance premiums differ from location to location? Test appropriate hypothesis using a =0.05. Consider locations as blocks. For full solution solve the problems 1, 2, 3, 4, and 5. 1. (2 marks) State the null and alternative hypotheses for a. and for b.2. (3 marks) Introduce the vector cost for the values of response variable, the vector Company for the levels A, B, C, D, and E of the factor Company, and the vector Location for the blocks 1, 2, 3, 4. Show the code, required for question 2, in blue or red, and corresponding R output in black. 3. [4 marks} Represent the results of analysis of variance by generating ANOVA table. Show the code, required to generate ANOVA table in blue or red, and corresponding R output in black. Make the conclusions about the differences in mean insurance premiums for different companies, and about the differences in the mean insurance premiums for different locations. 4. (3 marks) Perform Tukey's HSD test for the difference between mean insurance premiums for different companies (treatment means). Show the code, required to perform Tukey's HSD test, in blue or red, and corresponding R output in black.Analyzing the signs of differences B-A, C-A, D-A, E-A, C -B, D-B, E-B, D-C, E-C. and E-D, place the values of the means of insurance premiums for the companies A, B, C, D, and E into ascending order.5.{3 marks) Draw the diagram for population means ofinsurance premiums for the companies A, B, C, D, and E. In the diagram place population means in ascending order and underline the population means which are not significantly different. To draw the diagram, state p-values for the Tukey's HSD test, and show whether they are smaller or larger than 0.05. Mark the pairs of means that are not significantly different. p- value state whether p-value is mark the means which are smaller or larger than 0.05 not significantly different MMUMUOMUOW | DOOUUUUUUW-PEPD? Draw the diagram underlining the population means which are not significantly different