Use SPSS to answer the questions below. Interpret the output: running the test alone will not give you full credit. Keep in mind the requirements spelled out at the beginning of this assignment as well for any hypothesis testing questions.

1. A marketing research organization is interested to know the effects of four different advertising methods on monthly sales of a product. The company employed a statistician and he conducted a study with three cities, in which each city uses each of the four methods. The data for sales (in $1000) are given below. 

                 City

                      A    B     C

Advertising 1   130    120    130

Methods     2   135    125 120

             3   120    100    100

             4   100     96  90

a. Is this study an observational study or an experimental study? Explain.

b. Identify the experimental design used in this study. Explain.

c. Run an analysis using SPSS and test the hypothesis that no difference exist among the effects of the advertising methods (groups) on mean monthly sales. In other words, can you conclude that the different advertising methods have different effects on mean monthly sales. Set alpha = 0.05.

d. Can you conclude that the different cities have different effects on mean monthly sales? Set alpha = 0.05.

Your answers for (c) and (d) should be justified with null and alternate hypothesis, test statistic value and p value. You need not to do any calculation, use SPSS output instead.

e. Compute the relative efficiency of randomized block design and completely randomized design. Interpret this value. Were the blocking variable or variables effective in reducing the variability in experimental units? Explain. 

2. Consider a hypothetical experiment to investigate the effects of various diets on milk production in cows. The four diets (A, B, C and D) were fed to each of cows 1,2, 3 and 4 for four weeks continuously, and the total yield of milk produced in the last week is recorded. This experiment lasted for 16 weeks. The data are given below. 

                Cow 1     Cow 2            Cow 3         Cow 4

Period 1 A (142) B (214) C (287) D (253)

Period 2 B (153) A (207) D (221) C (217)

Period 3 C (193) D (195) B (248) A (178)

Period 4 D (167) C (232) A (214) B (146)

a. Identify the blocking variables in this study.

b. Write a statistical model appropriate to this experiment.

c. Use SPSS to run the analysis of this study. Use alpha = 0.05.

d. What conclusions can you draw about the best diet for cows?

e. Compute the relative efficiency of Latin square design and completely randomized design. Interpret this value. Were the blocking variables effective in reducing the variability in experimental units? Explain.

f. Plot normal plots and residual plots and check whether there is any indication of deviation from the assumptions of the study.