Question

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?

Answer 1

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

T₁ (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 = G²/N = 3028² / 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.