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ECON7300: Statistical Project Assignment (Part I), Semester 1, 2022

Instruction:

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

(B) Use the Excel  files Dataset9 and Dataset2 to answer questions asked in Part A and ‘Dataset3’and Dataset8’ 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 Dataset9 test at a 5% level of significance if there is any evidence of a significant difference in the average weight loss (in kg) for people in three groups defined by age category (agec). Follow all the necessary steps to perform the test and verify your results using Excel/PHStat. Note: in your data, the variable agec” is coded 1 for people aged 20- 29, 2 for people aged 30-39 and 3 for people aged 40-49.

(2) If your results in (1) indicate that it is appropriate, use the Tukey-Kramer procedure to determine  which  groups  of agec differ  in  average  weight  loss.  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 1% level of significance if there is any evidence of a significant difference in the average exam score (score) for grade 7 students in five groups defined by their class (class). Follow all the necessary steps to perform the test and verify your results using Excel/PHStat. Note: in your data, the variable “class” is coded 1 for students in class 7A, 2 for students in class 7B, 3 for students in class 7C, 4 for students in class 7D and 5 for students in class 7E.

(4) If your results in (3) indicate that it is appropriate, use the Tukey-Kramer procedure to determine  which  groups  of class differ  in  average  exam  score.  Use  a  1%  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.   The mobile industry is involved in a fierce battle for customers, with each company devising its own complex pricing plan to lure customers. Since a cost of a mobile phone minute varies drastically depending on the number of minutes per month used by the customer, a consumer watchdog group decides to compare the average cost for four mobile phone companies using four different usage levels as blocks. The monthly costs (in dollars) computed by the mobile companies for peak-time caller at very low (20 minutes per month), low (80 minutes per month), middle (300 minutes per month), and high (1000 minutes per month) usage levels are given in Dataset3. Hint: the blocking variable (usage level) is coded 1 if very low, 2 if low, 3 if middle and 4 if high.

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 monthly cost (cost) of the four treatments (i.e., four mobile phone companies)? Follow all the necessary steps to perform the test.

(c) If your results in (b) indicates that it is appropriate, use the Tukey procedure to determine which groups differ in the mean monthly cost. Use a 1% level of significance. Follow all the necessary procedure to perform the test.

2.   Suppose a firm would like to conduct a study comparing the prices of televisions made by different manufacturers (manu). Dataset8 contains data on prices of a random sample of

televisions for various screen sizes (ssize). Hint: the variable ssize is the blocking variable. 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 price of televisions made by different manufacturers (manu)? Follow all the necessary steps to perform the test.

(c) If your results in (b) indicates that it is appropriate, use the Tukey procedure to determine which groups differ in the mean television price. Use a 5% level of significance. Follow all the necessary procedure to perform the test.