Recall in Midterm Exam 1 we studied an investment advisory company? This questio

Question

Recall in Midterm Exam 1 we studied an investment advisory company? This question is about the same company. For your information, the description of the company and its data set is given again below: 8 points

An investment advisory company studied funds available on the market: Large cap, mid-cap, and small-cap. The company randomly selected some funds and measured their 1-year return rate (2011-2012) and 3-year return rate (2011-2014), respectively. Data is supplied in both Minitab and Excel format.

Your manager is interested in learning whether there is any difference among the three funds’ average 3-year return rate?                                                     5 points

If so, how is each type of fund different from others (Hint: A pairwise comparison).   3 points

P.S. Your manager says that a Minitab (or another statistical software package) report with a conclusion is fine. He is happy with a significance level of 0.05.   

1YrReturn%_Large 3YrReturn%_Large 1YrReturn%_Mid-Cap 3YrReturn%_Mid-Cap 1YrReturn%_Small 3YrReturn%_Small 28.99 24.26 26.38 18.70 22.70 19.47 33.40 22.72 15.77 16.25 14.86 16.23 33.98 21.91 16.16 15.65 17.59 16.12 33.78 21.89 16.27 15.26 9.99 15.83 21.62 16.47 16.94 15.04 16.24 14.96 22.87 16.10 14.60 15.02 8.75 14.94 17.41 13.44 11.40 14.97 15.48 14.90 16.54 13.30 16.64 14.61 12.85 14.66 15.72 13.16 14.75 14.56 11.07 14.23 14.50 12.59 17.80 14.44 14.32 14.14 17.14 12.45 16.95 14.17 16.74 13.85 15.23 12.39 15.69 13.78 10.46 13.48 18.62 12.16 15.61 13.78 8.60 13.47 22.45 12.15 17.80 14.44 10.39 13.22 15.66 12.14 16.95 14.17 10.85 13.07 13.75 11.97 15.69 13.78 9.40 12.90 14.62 11.84 15.61 13.78 10.88 12.84 26.06 11.80 23.24 13.55 16.38 12.76 15.72 11.44 10.46 13.50 11.33 12.67 11.86 11.29 19.73 13.50 11.98 12.63 18.64 11.21 16.43 13.49 8.82 12.52 15.71 11.13 14.71 13.40 12.35 12.48 17.77 11.07 18.57 13.31 7.28 12.40 15.36 11.07 14.40 13.26 12.90 12.36 17.33 11.04 17.61 13.24 12.99 12.23 21.08 10.90 16.40 13.01 11.44 11.60 18.12 10.86 18.28 12.94 14.92 11.50 9.16 10.83 10.34 12.92 13.01 11.28 22.02 10.68 15.08 12.71 10.83 11.22 16.63 10.67 15.96 12.69 11.79 11.17 13.08 10.62 12.16 12.60 16.75 11.14 12.49 10.56 16.04 12.53 10.25 10.75 17.72 10.54 18.36 12.03 12.71 10.57 13.42 10.52 10.90 11.81 12.55 10.54 14.18 10.43 9.82 11.72 6.64 9.94 16.99 10.35 12.26 11.64 12.70 9.74 13.12 10.11 13.78 11.60 20.50 9.52 14.74 10.07 15.46 11.53 2.54 9.18 17.93 10.06 11.97 11.52 9.92 9.16 12.27 10.02 14.93 11.50 8.78 8.71 11.29 10.01 14.45 11.49 6.73 7.62 10.75 10.00 10.88 11.42 13.65 7.49 12.57 9.95 12.18 11.27 6.47 6.61 17.67 9.92 12.20 11.16 10.48 6.57 13.60 9.92 9.45 10.91 9.15 6.56 12.18 9.75 7.74 10.86 16.55 5.96 18.31 9.74 13.80 10.34 2.88 5.47 17.07 9.69 15.31 10.73 9.01 5.45 14.88 9.67 21.46 10.39 7.06 5.38 15.13 9.65 13.69 10.20 6.03 5.12 15.02 9.64 13.93 10.08 3.70 3.60 11.17 9.56 12.91 10.04 9.37 3.41 20.67 9.52 2.43 9.78 26.67 19.88 16.79 9.46 12.86 9.71 5.75 14.69 19.91 9.46 12.94 9.60 17.74 13.80 13.23 9.45 15.46 9.58 18.53 13.13 9.99 9.44 11.39 9.09 20.54 12.25 19.95 9.34 5.70 8.65 12.18 12.11 14.82 9.30 9.97 8.54 14.94 12.09 16.57 9.25 11.78 8.54 20.94 11.76 20.85 9.19 8.13 8.19 11.47 11.41 12.40 9.11 4.23 7.99 10.89 11.08 11.80 9.07 5.97 7.26 14.23 10.82 15.67 8.97 12.60 7.11 10.19 10.40 12.72 8.90 7.85 7.00 15.60 10.23 11.75 8.78 6.77 6.97 7.27 9.63 15.27 8.70 11.47 6.18 16.52 8.96 12.99 8.47 3.80 6.02 10.87 8.88 15.83 8.42 22.44 5.26 12.23 8.72 13.39 8.42 -11.28 1.17 14.19 8.58 13.70 8.40 2.03 1.05 13.70 7.43 9.77 8.34 9.11 -1.63 3.23 7.12 16.95 8.21 20.19 14.77 11.21 8.16 19.14 12.67 17.23 8.16 19.37 12.50 9.23 8.12 15.71 12.28 13.42 8.09 22.19 12.18 14.05 7.99 20.21 12.04 12.70 7.96 18.24 12.04 13.96 7.89 21.90 11.61 13.54 7.89 16.44 11.39 13.44 7.88 15.30 11.11 14.09 7.81 18.67 11.01 16.04 7.75 15.57 10.77 16.65 7.64 19.09 10.53 11.80 7.64 12.39 10.53 16.13 7.63 16.03 10.20 14.26 7.24 10.51 8.65 17.74 7.21 11.65 8.19 12.99 7.12 13.06 7.51 15.77 7.03 13.31 5.02 12.25 6.90 14.65 6.62 12.97 6.52 11.28 5.92 11.72 5.63 13.02 5.61 19.40 5.50 10.32 5.35 11.56 4.70 14.29 4.58 8.85 3.70 7.84 1.18 15.05 12.40 10.02 12.28 20.44 11.96 14.75 11.85 17.80 10.81 6.77 10.52 14.50 10.47 17.22 10.45 19.85 10.34 9.40 10.30 11.94 10.27 19.09 10.11 13.65 10.10 9.00 9.93 13.80 9.91 18.68 9.62 16.41 9.43 13.58 9.42 14.55 9.33 14.51 9.26 16.38 9.22 13.67 9.03 16.33 9.03 15.66 8.83 15.61 8.78 17.23 8.76 16.51 8.51 15.34 8.35 16.58 8.32 15.43 8.31 15.92 8.30 9.23 8.23 16.25 8.22 14.70 8.19 8.73 8.12 19.32 7.87 14.60 7.74 14.25 7.54 6.36 7.47 9.47 7.23 10.86 6.80 5.98 6.70 16.81 6.01 10.55 5.68 6.60 5.57 13.85 5.56 11.42 5.48 1.67 4.87 13.83 4.84 9.34 2.37

Explanation / Answer

1. Ans: According to question, manager want to check whether there is any difference among the three funds’ average 3-year return rate. So, only data from 3-year return rate are used.

One-way ANOVA: Fund versus Market

Source DF SS MS F P
Market 2 217.6 108.8 10.33 0.000
Error 313 3297.3 10.5
Total 315 3514.9

S = 3.246 R-Sq = 6.19% R-Sq(adj) = 5.59%

Conclusion: The calculated p-value is 0.0000 and less than 0.05 table value. Hence, we can conclude that there is significant different of returns among the means of "large", "mid-cap" and "small" markets.

All Pairwise Comparisons among Levels of Market

Simultaneous confidence level = 87.97%

Market = Large subtracted from:

Market Lower Center Upper -+---------+---------+---------+--------
Mid_cap 0.841 1.687 2.532 (--------*-------)
Small 0.713 1.626 2.538 (--------*--------)
-+---------+---------+---------+--------
-1.0 0.0 1.0 2.0

Comment (1) : In the above table, all the confidence interval have same positive sign. Hence, the Large market is significantly differnt from the Mid_cap and Small market. Also, the mean return rate in Large market is lesser than the Mid-cap and Small markets.

Market = Mid_cap subtracted from:

Market Lower Center Upper -+---------+---------+---------+--------
Small -1.068 -0.061 0.946 (---------*---------)
-+---------+---------+---------+--------
-1.0 0.0 1.0 2.0

Comment (2): The confidence interval have differents sign in upper and lower end ponits. Hence, there is not significant different in the return rates between the Mid-cap and Small markets.

From comment (1) and (2), the return rate is high in Mid-cap and Small market than the Large market and there is no significant different between the Mid-cap and Small markets.

All the paire-wise comparision is done using 0.05 level of significance using Minitab software.

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