1. [31.5 pts] A portion of a data set containing information for 14 mutual funds that are part of the Morningstar Funds 500 for 2008 follows.
Fund Name Fund Type Net Asset Value ($) 5 Year Average Return (%) Expense Ratio (%) Morningstar Rank
Amer Cent Inc & Growth Inv DE 28.88 12.39 0.67 2-Star
American Century Intl. Disc IE 14.37 30.53 1.41 3-Star
American Century Tax-Free Bond FI 10.73 3.34 0.49 4-Star
American Century Ultra DE 24.94 10.88 0.99 3-Star
Ariel DE 46.39 11.32 1.03 2-Star
Artisan Intl Val IE 25.52 24.95 1.23 3-Star
Artisan Small Cap DE 16.92 15.67 1.18 3-Star
Baron Asset DE 50.67 16.77 1.31 5-Star
Brandywine DE 36.58 18.14 1.08 4-Star
Brown Cap Small DE 35.73 15.85 1.20 4-Star
Buffalo Mid Cap DE 15.29 17.25 1.02 3-Star
Delafield DE 24.32 17.77 1.32 4-Star
DFA U.S. Micro Cap DE 13.47 17.23 0.53 3-Star
Dodge & Cox Income FI 12.51 4.31 0.44 4-StarThe data set above includes the following five variables:
Type: The type of fund, labeled DE (Domestic Equity), IE (International Equity), and FI (Fixed Income).
Net Asset Value ($): The closing price per share on December 31, 2007.
5-YearAverageReturn(%): Theaverageannualreturnforthefundoverthepast5years.
ExpenseRatio(%): The percentage of assets deducted each fiscal year for fund expenses.
Morningstar Rank: The risk adjusted star rating for each fund; Morningstar ranks go from a low of 1-Star to a high of 5-Stars.a. Develop an estimated regression equation that can be used to predict the 5-year average return given fund type. (If you use Excel, you have to upload the file. Otherwise, no points will be given) [3 pts]____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
b. Use ? = 0.05 to test if the independent variable in the estimated regression equation from (a) is significant. Provide your reason. [4 pts]_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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c. What is the 99% confidence interval of ?1 for the estimated regression equation from (a)? [3.5 pts]
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d. Develop a 95% confidence interval to predict the mean 5-year average return given fund type FI. [10 pts] Hint: Use the regression equation from part a.
(1) Write down the formula calculating the confidence interval estimate of the mean 5-year average return given fund type FI:_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________(2) Start your calculation here:_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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e. Develop an estimated regression equation that can be used to predict the 5-year average return given the type of fund, the expense ratio, and the Morningstar Rank. You don’t need to remove any insignificant variables. What is the estimated regression equation? (If you use Excel, you have to upload the file. Otherwise, no points will be given) [5 pts]_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________f. (1) What is the value of adjusted multiple coefficient of determination for the estimated regression equation in (e)? [1.5 pts] _____________________________________________________________________________________
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(2) Explain the meaning of adjusted multiple coefficient of determination: [1.5 pts]
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g. Use ? = 0.05 to test if the independent variables in the estimated regression equation from (e) are significant. Provide your reason. [3 pts]_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
2. [13 pts] In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment.a. Complete the following ANOVA table. [7 pts]Source of Variation Sum of Squares Degrees of Freedom Mean Square F
Treatments 1200 (2) (5) (7)
Error (1) (3) (6) —
Total 1800 (4) — —(1) Write down the formula or concept calculating cell (1) and complete the calculation:
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(2) Write down the formula or concept calculating cell (2) and complete the calculation:
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(3) Write down the formula or concept calculating cell (3) and complete the calculation:
__________________________________________________________________________________________________________________________________________________________________________(4) Write down the formula or concept calculating cell (4) and complete the calculation:
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(5) Write down the formula or concept calculating cell (5) and complete the calculation:
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(6) Write down the formula or concept calculating cell (6) and complete the calculation:
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(7) Write down the formula or concept calculating cell (7) and complete the calculation:
__________________________________________________________________________________________________________________________________________________________________________b. At ? = 0.05 level of significance, is there a significant difference between the treatments? Why? [6 pts]__________________________________________________________________________________________________________________________________________________________________________
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3. [20.5 pts] A partial computer output from a regression analysis using Excel’s Regression tool follows.Regression Statistics
Multiple R (1)
R Square 0.923
Adjusted R Square (2)
Standard Error 3.35
Observations
ANOVA
df SS MS F Significance F
Regression (3) 1612 (7) (9)
Residual 12 (5) (8)
Total (4) (6)
Coefficients Standard Error t Stat P-value
Intercept 8.103 2.667
x1 7.602 2.105 (10)
x2 3.111 0.613 (11) a. Based on the given information above, complete the missing values (1) to (11). [5.5 pts]
Hint: It may not be necessary to follow the order to complete the table.(1) Write down the formula or concept calculating cell (1) and complete the calculation:
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(2) Write down the formula or concept calculating cell (2) and complete the calculation:
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(3) Write down the formula or concept calculating cell (3) and complete the calculation:
__________________________________________________________________________________________________________________________________________________________________________(4) Write down the formula or concept calculating cell (4) and complete the calculation:
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(5) Write down the formula or concept calculating cell (5) and complete the calculation:
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(6) Write down the formula or concept calculating cell (6) and complete the calculation:
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(7) Write down the formula or concept calculating cell (7) and complete the calculation:
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(8) Write down the formula or concept calculating cell (8) and complete the calculation:
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(9) Write down the formula or concept calculating cell (9) and complete the calculation:
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(10) Write down the formula or concept calculating cell (10) and complete the calculation:
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(11) Write down the formula or concept calculating cell (11) and complete the calculation:
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b. Use ? = .05. Test for overall significance. [6 pts]
(1) Formulate the null and alternative hypotheses for this test (fill in the blanks below).
H0 = ____________
Ha = ____________
(2) What is the p-value for the overall significance test? (If you use Excel, provide the function you use)
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(3) Use ? = 0.05. Do you reject or not reject H0? What is your conclusion?
(3.1) Write down the rejection rule: ________________________________________________________
(3.2) Write down your decision: __________________________________________________________
(3.3) Interpret your result: _______________________________________________________________
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c. Use ? = .05. Test for individual significance. [6 pts]
(1) Formulate the null and alternative hypotheses for this test (fill in the blanks below).
H0 = ____________
Ha = ____________
(2) What is the p-value of the test? (If you use Excel, provide the function you use)
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(3) Use ? = 0.05. Do you reject or not reject H0? What is your conclusion?
(3.1) Write down the rejection rule: ________________________________________________________
(3.2) Write down your decision: __________________________________________________________
(3.3) Interpret your result: _______________________________________________________________
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d. Based on the results in part (c), will you include both variables x1 and x2 in the regression model? Why or why not? [3 pts]
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4. [16 pts] A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow. The manufacturer’s suggested retail prices for the two models show a $10 price differential. Use ? = 0.05 level of significance and test that the mean difference between the prices of the two models is $10.Retail Outlet Deluxe Standard
1 39 27
2 39 28
3 45 35
4 38 30
5 40 34
6 39 30
7 35 29a. Formulate the null and alternative hypotheses that can be used to test that the mean difference between the prices of the two models is $10. (fill in the blanks below). [2 pts]H0 = ____________
Ha = ____________b. What is the test statistic? [4 pts]
(1) Write down the formula calculating the test statistic: _______________________________________
(2) Start your calculation here: ____________________________________________________________
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c. What is the p-value? (If you use Excel, provide the function you use) [4 pts]
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d. What is the critical value based on ? = 0.05? (If you use Excel, provide the function you use) [4 pts]
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e. Use ? = 0.05. Do you reject or not reject H0? What is the rejection rule you use? What is your conclusion. [2 pts]
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5. [19 pts] Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use ? = 0.05 and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
n1=16 n2=10
6.82
6.25s1=.64 s2=.75a. State the null and alternative hypotheses that can be used to test whether the consultant with more experience has the higher. (fill in the blanks below). [2 pts]H0 = ____________
Ha = ____________
Definition of notations:__________________________________________________________________________________________________________________________________________________________________________
b. What is the test statistic? [4 pts](1) Write down the formula calculating the test statistic: _______________________________________
(2) Start your calculation here: ____________________________________________________________
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c. What is the p-value of the test? (If you use Excel, provide the function you use) [4 pts]
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________d. What is the critical value based on ? = 0.05? (If you use Excel, provide the function you use) [4 pts]
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e. Use ? = 0.05. Do you reject or not reject H0? What is the rejection rule you use? What is your conclusion. [2 pts]
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f. Develop a 95% confidence interval for the difference between the two population mean service ratings. [3 pts]_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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