Question

# Sample scores from four different statistics class sections are shown below. Run an ANOVA test on...

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

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) = F0.05,(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.