ECON7300
Statistical Project: Part I
Semester 1, 2024
Section A
Note: For questions in Section A, assume the assumptions underlying ANOVA (i.e., randomness and independence, normality, and homogeneity of variance) are met. Use the closest degrees offreedom for the denominator to get critical values from the F-table and to find QU in the studentised range Q-table.
(1) Using Part1_Dataset9, test at a 5% level of significance if there is any evidence of a significant difference in the average weekly wage income in Indian rupees (wage) for workers in four groups defined by their age in years (age). Follow all the necessary steps to perform the test and verify your results using Excel/PHStat. Note: In your data, the variable “age” is coded 1 for workers younger than 30 years, 2 for those aged 30-39 years, 3 for 40-49 years, and 4 for 50 years or older.
(2) If your results in (1) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which age groups differ in average weekly wage income. Use a 5% level of significance. Follow all the necessary steps to perform. the test and verify your results using Excel/PHStat.
(3) Using Part1_Dataset10, test at a 1% level of significance if there is any evidence of a significant difference in the average price of fish (price, in US dollars) at the Futon Fish Market with sales in three groups defined by recent weather conditions (weather). Follow all the necessary steps to perform. the test and verify your results using Excel/PHStat. Note: In your data, the variable “weather” is coded 1 for good weather conditions in the mostrecent five days, 2 for windy weather, and 3 for stormy weather.
(4) If your results in (3) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which groups of weather conditions differ in the average fish price. Use a 1% level of significance. Follow all the necessary steps to perform. the test and verify your results using Excel/PHStat.
Section B
Note: For questions in Section B, assume the assumptions underlying ANOVA (i.e., randomness and independence, normality, and homogeneity of variance) are met. Use the closest degrees offreedom for the denominator to get critical values from the F-table and to find QU in the studentised range Q-table.
(1) A car rating website asked ten car experts to rate four Japanese car brands. The experts had to provide a satisfaction rating (out of 100) for each brand: Mazda (coded 1), Honda (coded 2), Subaru (coded 3), and Toyota (coded 4). The file Part1_Dataset11 displays the ratings for the different brands for each car expert. Hint. The variable “expert” is the blocking variable.
Based on the information given, answer the following questions.
(a) At the 5% level of significance, is blocking effective? Follow all the necessary steps to perform. the test and verify your results using Excel/PHStat.
(b) Using a 5% level of significance, is there a significant difference in the mean rating score of the four brands? Follow all the necessary steps to perform. the test and verify your results using Excel/PHStat.
(c) If your results in (b) indicate that it is appropriate, use the Tukey procedure to determine which brands differ in the mean rating score. Use a 5% level of significance. Follow all the necessary steps to perform. the test.
(2) How does a company’s size affect the salary of its chief executive officer (CEO)? Since CEO
salaries vary according to the type of company they work at, a data scientist decides to compare average CEO salaries (salary, in thousands of US dollars) for three company sizes (size) using four types of companies (type) as blocks. In Part1_Dataset12, size is coded 1 for small companies, 2 for medium companies, and 3 for large companies. The blocking variable (type) is coded as 1 for industrial companies, 2 for financial companies, 3 for those producing consumer products, and 4 for transportation or utility companies.
Based on the information given, answer the following questions.
(a) At the 1% level of significance, is blocking effective? Follow all the necessary steps to perform. the test and verify your results using Excel/PHStat.
(b) Using a 1% level of significance, is there a significant difference in the mean salary of the different company sizes? Follow all the necessary steps to perform the test and verify your results using Excel/PHStat.
(c) If your results in (b) indicate that it is appropriate, use the Tukey procedure to determine which company sizes differ in the mean salary. Use a 1% level of significance. Follow all the necessary steps to perform. the test.