7) A math test is given to 6-, 7-, and 8-year-old boys and girls. The results ar
ID: 3365700 • Letter: 7
Question
7) A math test is given to 6-, 7-, and 8-year-old boys and girls. The results are given below. The researcher wants to determine if gender, age, or both impact the test score. Assume the scores represent continuous data.
a. What are your hypotheses for this test?
b. What test would you use to test these hypotheses?
c. Perform the test.
d. Which hypotheses do you reject and which do you accept? Justify your answer.
Gender Score Age Grou 6-year-olds 6-year-olds 6-year-olds 6-year-olds 6-year-olds 6-year-olds 7-year-olds 7-year-olds 7-year-olds 7-year-olds 7-year-olds 7-year-olds 8-year-olds 8-year-olds 8-year-olds 8-year-olds 8-year-olds 8-year-olds Girl Girl Girl Girl Girl Girl 10 13 Girl Girl Girl 13 12 14 16Explanation / Answer
Result:
a. What are your hypotheses for this test?
To test gender, age, or both impact on the test score.
b. What test would you use to test these hypotheses?
Two way ANOVA to bo used.
c. Perform the test.
Two factor ANOVA
Factor 2 age
Means:
age6
age7
age8
boy
6.0
7.0
10.0
7.7
Factor 1 gender
girl
7.0
10.0
14.0
10.3
6.5
8.5
12.0
9.0
3
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1 gender
32.00
1
32.000
5.65
.0350
Factor 2 age
93.00
2
46.500
8.21
.0057
Interaction
7.00
2
3.500
0.62
.5555
Error
68.00
12
5.667
Total
200.00
17
d. Which hypotheses do you reject and which do you accept? Justify your answer.
To test the gender effect, calculated F=5.65, P=0.035 which is < 0.05 level. Ho is rejected.
Gender is significant effect on test score.
To test the age effect, calculated F=8.21, P=0.0057 which is < 0.05 level. Ho is rejected.
Age is significant effect on test score.
To test the interaction of age and gender effect, calculated F=0.62, P=0.5555 which is >0.05 level. Ho is not rejected.
Interaction is not significant effect.
Two factor ANOVA
Factor 2 age
Means:
age6
age7
age8
boy
6.0
7.0
10.0
7.7
Factor 1 gender
girl
7.0
10.0
14.0
10.3
6.5
8.5
12.0
9.0
3
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1 gender
32.00
1
32.000
5.65
.0350
Factor 2 age
93.00
2
46.500
8.21
.0057
Interaction
7.00
2
3.500
0.62
.5555
Error
68.00
12
5.667
Total
200.00
17
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