M1-Tradtional M2 - Power Point M3 - Hybrid M4 - Self Students 60 60 60 60 Averag
ID: 3205126 • Letter: M
Question
M1-Tradtional
M2 - Power Point
M3 - Hybrid
M4 - Self
Students
60
60
60
60
Average
83.767
85.150
82.767
83.683
St. Dev
6.323
5.854
5.998
6.302
Need help doing the F dist.
Within group estimate for the variance is: 27.22
Between group estimate for the variance is 10.5
Use the F statistic to determine if all the instruction methods are the same or if there is a difference in performance of the students under the dfferent methods (be sure to show 6 hypothesis steps)
M1-Tradtional
M2 - Power Point
M3 - Hybrid
M4 - Self
Students
60
60
60
60
Average
83.767
85.150
82.767
83.683
St. Dev
6.323
5.854
5.998
6.302
Explanation / Answer
Solution:
Step 1
Hypothesis:
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is no any significant difference in the average performance of the students under the four different methods.
Alternative hypothesis: Ha: There is a significant difference in the average performance of the students under the four different methods.
Step 2
Significance level:
Let us assume the level of significance or alpha value as 0.05.
Step 3
Test Statistic:
Now, we have to find the value for test statistic F. The formula for F test statistic is given as below:
F = variance between treatments / variance within treatments
F = 10.5/27.22 = 0.385745775
F = 0.385745775
Step 4
Critical value and P-value:
Degrees of freedom for between treatments = 4 – 1 = 3
Degrees of freedom for within treatments = (60*4) – 1 – 1 = 240 – 1 – 3 = 239 – 3 = 236
Now, by using above degrees of freedom and F table we have to find the critical value and P-value which is given as below:
Critical value = 2.642851061
P-value = 0.7634
Step 5
Decision:
P-value = 0.7634 > Alpha value = 0.05
So, do not reject the null hypothesis
Step 6
Conclusion:
We conclude that there is no sufficient evidence that there is a significant difference in the average performance of the students under the four different methods.
There is sufficient evidence that there is no any significant difference in the average performance of the students under the four different methods.
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