A study was conducted to investigate the relationship between the scores of three mathematics exams, namely algebra, geometry, and calculus. The data for 50 students were collected and analyzed using a one-factor analysis. The following is the output of the analysis:

• Total sum of squares = 6000
• Sum of squares due to the factor = 3800
• Sum of squares due to error = 2200
• Degrees of freedom for the factor = 2
• Degrees of freedom for error = 147
• Mean square due to the factor = ?
• Mean square due to error = ?
• F-ratio = ?
• Critical F-value = 2.45
• Conclusion = ?

a) Calculate the mean square due to the factor and the mean square due to error. (4 marks)

b) Calculate the F-ratio. (4 marks)

c) Determine whether the F-ratio is significant at the 5% level of significance. (4 marks)