Exercise 3 (32 marks = 6 + 14 + 10 + 2) A consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid laundry detergent was carried out in four supermarkets (1, 2, 3, and 4). These four supermarkets were supplied with the new liquid laundry detergent in all three bottle designs. The new liquid laundry detergent was priced the same, irrespectively of the supermarket and the bottle design. The table below shows the number of bottles of new liquid laundry detergent sold in a 24-hour period at each supermarket. The same data are saved in the a2e3.xisx file.Daily sales Bottle Design A B C 16 33 23 N - Supermarket 14 30 21 3 1 19 8 4 6 23 12 The study aims to find out whether there are differences in mean daily sales across the bottle designs, or across the supermarkets.(a) (6 marks) What is the variable of interest? Is it qualitative or quantitative? If it is qualitative, is it ranked or unranked? If it is quantitative, is it discrete or continuous? What is its level of measurement? What is the experimental design? Explain your answers. (b) (14 marks) Are there differences between the effects of the bottle designs on mean daily sales? Are there differences between the effects of the supermarkets on mean daily sales? Answer these questions by performing appropriate parametric tests at the 5% significance level with R. State the hypotheses, report the observed test statistics, make statistical decisions, and draw the implied conclusions. (c) (10 marks) Suppose that you are advised that the required conditions of the parametric tests you ran in part (b) might not be fully satisfied. Answer the questions in part (b) by performing this time appropriate nonparametric tests at the 5% significance level with R. State the hypotheses, report the observed test statistics, make statistical decisions, and draw the implied conclusions. (d) (2 marks) Compare the tests you ran in parts (b) and (c) to each other. Do they lead to the same or different conclusions? What if the significance level is reduced to 1%? Explain your answers