Question 2 - Utility Bills Supposed that, when comparing utility bills, a researcher was interested in determining whether residential utility bills differed among different cities in Canada, and also whether they differed depending on the number of bedrooms in a house. As part of the study, a random sample of households in different Canadian cities was selected, and their monthly utility bills and number of bedrooms were recorded. The data is provided in the dataset Utility Bills. a) Plot the residuals against the fitted values corresponding to the two-way ANOVA model for this analysis. What two key model assumptions can be examined with this plot and do they appear to be warranted? b) Test the following hypothesis at the 1% significance level; make sure you follow all the steps for hypothesis testing indicated in the Instructions section. Use software to generate the corresponding two-way ANOVA table, but show any other computations. Significant interaction effect between number of bedrooms and city; . Significant main effect of the number of bedrooms factor (if warranted); . Significant main effect of the city factor (if warranted). c) Create the corresponding interaction plot and explain if it shows interaction between number of bedrooms and city. Is this consistent with your results for part b) above? d) Calculate the Bonferroni margin of error for the confidence intervals based on all pairwise differences between the treatment means. Show your manual calculations and use an overall 95% confidence level. e) Using the calculated margin of error from part d) and the pairwise confidence interval approach, determine whether there is sufficient evidence (at the 5% significance level) of a difference in mean monthly utility bills between 2-bedroom houses in Ottawa and 2- bedroom houses in London