An education researcher is interested in students’ motivation tostudy local history. The researcher believes that if studentsexperience a particular form of positive coaching, then they willbe more likely to show interest in local history.

This researcher is testing two hypotheses. The first is that thecoaching boosts self-efficacy and has an effect on students’motivation. The second is that this treatment effect is moderatedby year in school. Past research has suggested that there shouldnot be a main effect for school year. However, to control for thispossibility, a 2-way (2x2) factorial ANOVA is being conducted toaccount for any influence from school year, the treatment, and theinteraction of the two main effects.

To test the hypotheses, the research has obtained 28 participants:14 year-7 students and 14 year-10 students. From each group of 14,7 students were randomly chosen for the treatment group. After thetreatment, all students were given the same test. This test hasbeen used in previous research, has a range of 0 to 100, andmeasures students’ interest in issues relating to local history.(The higher the test score, the more positive the result.)

Use a 2x2 ANOVA with α=0.02α=0.02 to test the the data and evaluatethe hypotheses. Results are provided below for each group ofstudents.

	Factor B: Treatment
Control: No Coaching	Treatment: Positive Coaching
Factor A: School Year	Year 7	64.5 66.3 71.2 79.8 43.2 58.5 49.6	74.3 74.6 85.6 82.5 72.3 72.4 87.9
Year 10	69.9 65.4 62.9 68.4 69.7 81.8 66.8	83.2 82.8 76.0 80.5 79.1 76.2 84.3

( 1a ) What is the F value for thetreatment effect?  
(Report answer accurate to 2 decimal place.)

( 1b ) What is the p-value for theF value for the treatment effect?  
(Report answer accurate to 4 decimal places.)

( 1c ) Does this support the researcher'shypothesis that the treatment has an effect on interest in localhistory?

• yes
• no

( 2a ) What is the F value for theschool-year effect?  
(Report answer accurate to 2 decimal place.)

( 2b ) What is the p-value for theF value for the school-year effect?  
(Report answer accurate to 4 decimal places.)

( 2c ) Does this support the researcher'sassumption that school-year does NOT have aneffect on interest in local history?

• yes
• no

( 3a ) What is the F value for theinteraction effect?  
(Report answer accurate to 2 decimal place.)

( 3b ) What is the p-value for theF value for the interaction effect?  
(Report answer accurate to 4 decimal places.)

( 3c ) Does this support the researcher'shypothesis that the treatment effect is moderated byschool-year?

• yes
• no

( 4 ) Based on these findings, which group can yousay had the higher average on the test?

• year-7 students
• year-10 students
• group with no coaching
• group with positive coaching
• year-7 students in the control group
• year-10 students in the control group
• year-7 students in the treatment group
• year-10 students in the treatment group