Sample scores from four different statistics class sections are shown below. Run an ANOVA test on them and answer the following questions:
Class 1 | Class 2 | Class 3 | Class 4 |
95 | 79 | 77 | 81 |
99 | 68 | 91 | 96 |
75 | 84 | 84 | 68 |
76 | 78 | 84 | 89 |
82 | 74 | 75 | 78 |
97 | 93 | 82 | 75 |
93 | 95 | 82 | 88 |
83 | 88 | 85 | 98 |
86 | 95 | 96 |
59 |
What conclusion can we make about the hypothesis test?
Hypothesis:
Ho: There is no significant differences in four different statistics class sections.
Ha: There is significant differences in four different statistics class sections.
CALCULATION:
Number of Treatment, t = 4 n = 36
T_{1} (sum of Class 1 ) = 786, T2(Sum of Class 2) = 754, T3(Sum of Class 3 ) = 756, T4(Sum of Class 4 ) = 732
G = Grand Total = 3028
CF = Correction Factor = G^{2}/N = 3028^{2} / 36 = 254688.4
= (95)^{2} + (79)^{2} + ......................+ (59)^{2} - 254688.4
= 257914 - 254688.4
TSS = 3225.556
SSTR = (1 / 9) * [(786)^{2} + (754)^{2} + (756)^{2} + (732)^{2} ] - 254688.4
SSTR = 164
SSE = SST - SSTR
= 3225.556 - 164
SSE = 3061.556
MSSTR = SSTR/t-1 = 164 / 4-1 = 54.67
MSSE = SSE / n-t = 3061.556 /36-4 = 95.67
F = MSSTR / MSSE = 54.67 / 95.67 = 0.57
Ftabulate = F ,(t-1,n-t) = F_{0.05,(3,32)} = 2.9011
ANOVA |
||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 164 | 3 | 54.67 | 0.571 | 0.6379 | 2.9011 |
Within Groups | 3061.556 | 32 | 95.67 | |||
Total | 3225.556 | 35 |
Conclusion:
, i.e. 0.571 < 2.9011, That is Fail to Reject Ho at 5% level of significance.
We conclude that data do not provide us any evidence against the null hypothesis Ho, and hence it may be accepted at 5%level of significance. That is,
There is no significant differences in four different statistics class sections.
Get Answers For Free
Most questions answered within 1 hours.