Question 1 [18 marks] The dividend yield of a share is the dividend per share divided by the price per share and is often expressed as a percentage. Historically, many investors consider a higher dividend yield to be desirable as it could be considered that the stock is underpriced. A survey on dividend yield was conducted to determine whether investors believe four (4) different banks to be equally investable. Twentyfour (24) investors were randomly divided into four groups of six. Each group will be focusing on a different bank. Each investor was then asked to forecast the dividend yield of that bank for the next financial year. For each group, an equal number of six (6) opinions were collected. The data recorded are the dividend yield of a corresponding bank (numbered from 1 to 4). a) Comment on two interesting features of the Dividend Yields data based on the boxplot below. Boxplot of Dividend Yields by Banks 81012 Dividend Yield % 6 b) Suppose you wish to perform a one-way ANOVA for the Dividend Yield data. Use the de- scriptive statistics below (from RStudio) to complete the ANOVA table below by filling the missing entries (missing entries are underlined). Also write down, in details, the expression (ie, showing all relevant numerical values not just mathematical symbols) for calculating the between-group sum of squares (ie, Treatment SS or SST). tapply (Yield, Bank, mean) # mean of yields by bank group # 1 2 3 4 # 10.380000 10.893333 9.906667 7. 040000 tapply (Yield, Bank, sd) # standard deviation of yields by bank group # 1 2 3 4 # 1. 264911 1. 032796 1. 471960 1. 643168 tapply (Yield, Bank, length) # sample size by bank group # 1 2 3 4 # 6 6 6 6 Source d.f. S.S. M.S. F-value Bank 9.47 Error 1.88 Total 91.19c) Based on the results in your completed ANOVA table above in part b), test if there is any difference in average yields across the four banks groups. Remember to state null and alternative hypotheses, give the test statistic value and associated degrees of freedom, p value or range of it, and draw your conclusion (assuming that all test assumptions are ok for this part). d) If someone wants to find out whether there is an}r difference in average yield between the first three banks (Bank 13) as a whole and the last one (Bank 4), form an appropriate contrast to evaluate and test the difference. Remember to state null and alternative hypotheses, give the test statistic value and associated degrees of freedom} the evidence for rejecting or not rejecting the null hypothesis with a conclusion. tapply(Yield, Bank, mean) # mean of Yield. by bank group # 1 2 3 4 # 10.380000 10.893333 9.906667 7.040000