Answer a
Given that the experiment has two factors (Factor Gender and Factor Education level ) at a = 2(Male and Female) and b = 2(less than bachelor degree and at least one bachelor degree) levels. Thus there are ab = 2× 2 = 4 different combinations of Gender and Education level.
With each combination r = 3 loads. r is called the number of replicates.This sums up to n = abr = 12 loads in total.
The Yijk denotes the no of observations for k (k = 1, 2, 3) with gender i (i = 1, 2) at education level j (j = 1, 2, 3) are recorded as follows
From the given data we can write
Less than bachelor's degree | Mean | At least one bachelor's degree | Mean | mGender | |||||
Male | 15 | 8 | 6 | 9.67 | 12 | 10 | 9 | 10.33 | 10.00 |
Female | 10 | 5 | 7 | 7.33 | 10 | 6 | 9 | 8.33 | 7.83 |
meducation | 8.50 | 9.333 | 8.92 |
DF error is n-ab = 12 - 4 = 8
MSE = SSE/ DF = 8.83
In similar way we can fill the ANOVA table
Variation | df | SS | Mean squares | F - Statistics | P-value |
Factor A(Gender) | 1 | 2.35 | 2.35 | 0.27 | 0.6200 |
Factor B(Education) | 1 | 0.35 | 0.35 | 0.04 | 0.8472 |
Interaction | 1 | 4.36 | 4.36 | 0.49 | 0.5023 |
Error | 8 | 70.67 | 8.83 | ||
Total | 11 | 77.72667 |
Answer b
Main Effect of Factor A(Gender):
H0:μM.=μF.
HA: not all μi. are equal where μi. is the mean for ith gender.
Now form ANOVA table we got the p value for Factor A is greater than 0.05.
Therefore we are unable to reject the null hypothesis at 0.05 level of significance and conclude that the no significant effect of gender .
Answer c
Main Effect of Factor B(Education level):
H0:μ.1=μ.2
HA: not all μ.j are equal where μi.is the mean for ith education
level
Again form ANOVA table we got the p value for Factor B is greater than 0.05.
Therefore we are unable to reject the null hypothesis at 0.05 level of significance and conclude that the there is not significant difference in education level as well.
Answer c
A × B Interaction:
H0: there is no interaction
HA: an interaction exists
ANOVA table says that p-value for interaction is also greater than 0.05 and we are unable to reject the null hypothesis.
Hence we can conclude that there no significant difference in education and gender together.
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