ECON7300: Statistical Project Assignment (Part I), Semester 2, 2022

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ECON7300: Statistical Project Assignment (Part I), Semester 2, 2022

Instruction:

(A) Questions in this paper should be answered by students whose surnames fall within the range A-K.

(B) Use the Excel  files  ‘Dataset1 and Dataset2’ to answer questions asked in Part A and ‘Dataset3’and ‘Dataset4’ to answer questions asked in Part B.

(C) A heavy penalty will be applied if your answers are not based on datasets assigned to you.


Part A:

Note: for questions in Part A assume that the three assumptions underlying     ANOVA (i.e., randomness and independence, normality and homogeneity of  variance) are met. If the degrees of freedom for the denominator are not on the table, use the closest value the table has.


(1) Using Dataset1 test at a 5% level of significance if there is any evidence of a significant difference in the average number of absences (absence) for professors in three groups defined by department (department). Follow all the necessary steps to perform the test and verify your results using Excel/PHStat. Note: in your data, “department” is coded 1 for professors in the department of Engineering; 2 for professors in the department of Economics, and 3 for professors in the department of Medicine.

(2) If your results in (1) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which groups of department differ in average number of absences. Use a 5% level of significance. Follow all the necessary steps to perform the test and verify your results using Excel/PHStat.

(3) Using Dataset2 test at a 5% level of significance if there is any evidence of a significant difference in the average contributions (contribution) made to United Way by three groups of managers defined by the type (type) of food business they manage. Note: in your data, the variable “type” is coded 1 if bakery, 2 if catering, and 3 if organic food shop.

(4) If your results in (3) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which groups of type differ in average contributions made to United Way. Use a 5% level of significance. Follow all the necessary steps to perform the test and verify your results using Excel/PHStat.


Part B

Note: for questions in Part B assume that the three assumptions underlying     ANOVA (i.e., randomness and independence, normality and homogeneity of  variance) are met. If the degrees of freedom for the denominator are not on the table, use the closest value the table has.


1.   An investor has consulted four different financial advisors (advisor) with regard to the expected annual rate of return (return) for each of four portfolio (portfolio) possibilities she is considering. The financial advisors have been chosen because they are known to range from very conservative (advisor  1) to very optimistic (advisor 4). The advisors’ respective estimates for the three portfolios are saved in Dataset3. Hint: the variable advisor  is  the  blocking  variable.  Portfolio  possibilities  are  aggressive  (coded  1),

speculative (coded 2), hybrid (coded 3) and defensive (coded 4).

Based on the information given, answer the following questions.

(a) At the 1% level of significance, was blocking effective? Follow all the necessary steps and verify your results using Excel/PHStat.

(b) Using a 1% level of significance, is there a significance difference in the mean expected annual rate of return (return) of portfolios in the four possibilities (portfolio)? Follow all the necessary steps to perform the test.

(c) If your results in (b) indicate that it is appropriate, use the Tukey procedure to determine which groups (i.e., portfolio possibilities) differ in the mean expected annual rate of return. Use a 1% level of significance. Follow all the necessary procedure to perform the test.

2.   A consumer group asked five drivers (driver) to drive four different models (model) of cars manufactured by Toyota in 2021 and report their satisfaction (satisfaction) levels out of 40. The rating is based on interior and comfort, exterior safety features, engine and gearbox, and reliability and build quality. The drivers’ ratings for the four models of Toyota cars are saved in Dataset4. Hint: the variable driver is the blocking variable. The four different models of cars are Toyota Yaris (coded 1), Toyota Camry (coded 2), Toyota Kruger (coded 3) and Toyota Prius (coded 4).

Based on the information given, answer the following questions.

(a) At the 5% level of significance, was blocking effective? Follow all the necessary steps

and verify your results using Excel/PHStat.

(b) Using a 5% level of significance, is there a significance difference in the mean satisfaction level (satisfaction) between the four models of Toyota cars? Follow all the necessary steps to perform the test.

(c) If your results in (b) indicate that it is appropriate, use the Tukey procedure to determine which groups (i.e., models of Toyota cars) differ in the mean satisfaction level. Use a 5% level of significance. Follow all the necessary procedure to perform the test.













2022-09-23