# 12.7 Assignment 12

## Purposes

The following questions have two parts. The first part assesses your knowledge of identifying cases where one-way ANOVA should be used, explaining the main idea of one-way ANOVA, and conducting a one-way ANOVA F test based on the computer outputs. The second part assesses your skills in using R Commander to conduct a one-way ANOVA F test.

## Resources

M12_Rent_ANOVA_Q5_FourColumnS.xlsx

## Instructions

**Part A**

Complete the following:

- What does ANOVA stand for? (2 marks)
- When shall we use a one-way ANOVA F test? (2 marks)
- Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are 10, 12, and 15. Determine the degrees of freedom for the
*F*statistic. (2 marks) - We stated earlier that a one-way ANOVA test is always right-tailed because the null hypothesis is rejected only when the test statistic, F, is too large. Why is the null hypothesis rejected only when F is too large? (3 marks)
- Fill in the missing entries in the following ANOVA table. (4 marks)

Source *df**SS**MS*= [latex]\frac{SS}{df}[/latex]F-statistic Treatment 2 ? 21.652 [latex]F_{o} = ?[/latex] Error ? 84.400 Total 14 ? - The data on monthly rents, in dollars, for independent random samples of newly completed apartments in the four U.S. regions are presented in the following table. (See the spreadsheet
**M12_Rent_ANOVA_Q5_FourColumnS.xlsx**)

**Northeast****Midwest****South****West**1005 870 891 1025 898 748 630 1012 948 699 861 1090 1181 814 1036 926 1244 721 1269 606 Given the ANOVA table, test at a 5% significance level whether a difference exists in the mean rent of newly completed apartments in the four U.S. regions. (8 marks)

Source *df**SS**MS*= [latex]\frac{SS}{df}[/latex]F-statistic P-value Region 3 400513 133504 [latex]F_{o} = 7.541[/latex] 0.0023 Error 16 283265 17704 Total 19 683778 - The following table gives the salaries (in thousand dollars) for computer science (CS) majors obtaining a bachelor’s degree, a master’s degree, or a Ph.D. (See the spreadsheet
**M12_Salary_ANOVA_Q7.xlsx**)

**Salary****Degree****Salary****Degree****Salary****Degree**50.8 Bachelor’s 65.8 Master’s 73.3 Ph.D 59.4 Bachelor’s 57.5 Master’s 65.7 Ph.D 55.9 Bachelor’s 66.9 Master’s 71.7 Ph.D 45.1 Bachelor’s 62.8 Master’s 72.5 Ph.D 54.1 Bachelor’s 68.5 Master’s 73.0 Ph.D 50.7 Bachelor’s 69.3 Master’s 67.2 Ph.D 46.8 Bachelor’s 61.5 Master’s 67.5 Ph.D - Fill in missing entries of the following ANOVA table. (4 marks)

Source *df**SS**MS*= [latex]\frac{SS}{df}[/latex]F-statistic P-value Degree ? ? 616.9 [latex]F_{o} = 34.62[/latex] < 0.0001 Error ? ? 17.8 Total 20 1554.5 - Test at the 1% significance level whether a difference exists in mean salary for computer science (CS) majors obtaining a bachelor’s degree, a master’s degree or a Ph.D. (8 marks)

- Fill in missing entries of the following ANOVA table. (4 marks)

**Part B**

**Finish the following questions using R and R commander**.

- Refer to Question 6 in Part A. The data are provided in the file
**M12_Rent_ANOVA_Q6.xlsx**. Import the data into R commander. Regenerate the ANOVA table in Question 6 in Part A. Make sure you copy and paste the computer output. (3 marks) - Refer to Question 7 in Part A. The data are provided in the file
**M12_Salary_ANOVA_Q7.xlsx**. Import the data into R commander. Obtain the ANOVA table and compare it with Question 7 in Part A. Make sure you copy and paste the computer output. (4 marks)