An education researcher is interested in students’performance on a mathematics test for a novel---and generallyunfamiliar---concept. The researcher believes that if studentsparticipate in an extracurricular training session, then they willbe more likely to perform better on the mathematics test.

This researcher is testing two hypotheses. The first is that thetraining session provides specific instruction and has an effect onstudents’ mathematics test scores. The second is that thistreatment effect is moderated by gender. Past research hassuggested that there should not be a main effect for gender.However, to control for this possibility, a 2-way (2x2) factorialANOVA is being conducted to account for any influence from gender,the treatment, and the interaction of the two main effects.

To test the hypotheses, the research has obtained 28 participants:14 boys and 14 girls. From each group of 14, 7 students wererandomly chosen for the treatment group. After the treatment, allstudents were given the same test. This test has been used inprevious research, has a range of 0 to 100, and measures students’ability to correctly perform the novel mathematics exercise. (Thehigher 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 Training	Treatment: Attend Training
Factor A: Gender	Male	67.6 60.0 65.4 67.3 57.6 43.1 61.3	61.6 69.3 70.5 56.6 64.2 60.5 62.6
Female	52.8 51.5 66.5 62.7 55.8 48.1 58.6	71.0 73.6 76.4 62.4 74.4 86.9 71.2

( 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 ability to solve themathematics exercise?

• yes
• no

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

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

( 2c ) Does this support the researcher'sassumption that gender does NOT have an effect onability to solve the mathematics exercise?

• 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 by gender?

• yes
• no