In: Statistics and Probability
Blood tests were performed on three groups of patients that had cornoavirus and suffered mild, severe or critical symptoms.
The immune system makes antibodies to protect the body from viruses and the levels of the IgG antibody was measured in each patient. IgG is the most common antibody in blood and the researchers wanted to examine if there were different levels within the three groups of patients and particularly in the critical group that eventually succumbed to the disease and died.
IgG can take time to form after an infection and values were recorded in the three groups on the 14th day after getting symptoms
The results are recorded in the following table.
IgG (AU/ml) 
Mild 
Severe 
Critical 

180 241 195 199 207 201 222 189 201 
150 175 180 201 168 175 192 195 
175 148 153 135 166 

Means 
203.8889 
179.5 
155.4 
StDev 
18.1207 
16.4838 
15.5981 
Ho: Average levels of IgG antibody are the same in the groups.
H1: Average levels of IgG antibody are different in the groups.
(a) Complete the ANOVA table. Use α=0.05 significance level.
(Round the SS and Variance values to 2 decimal places and Fteststatistic to 1 decimal place. Leave no cells blank)
Source of Variation 
Sums of Squares (SS) (2dp) 
DF 
Variance (2dp) 
F (1 dp) 

Between Groups  7811.9111  Answer  Answer  Answer 
Within Groups  Answer  Answer  Answer  
Total  Answer  21 
(b) 
Look up the critical value from
tables to answer the question below. 

There are Answer significant differences/not significant differences in the levels of IgG antibody across the groups. 
(1 Mark)
(a)
The ANOVA Table is completed as follows:
Source of Variation  Sum of Squares  DF  Variance  F 
Between groups  7811.9111  2  7811.9111/2=3905.96  3905.96/289.58=13.5 
Within groups  5502.0889  19  5502.0889/19=289.58  
Total  13314 
The entries in the Table are got as follows:
From the given data the following Table is calculated:
Mild  Severe  Critical  
n  9  8  5 
Sum  1835  1436  777 
Mean  203.889  179.5  155.4 
376763  259664  121719  
Std. Dev.  18.121  16.484  15.598 
SS  2626.889  1902  973.2 
(b)
Calculated value of F = 3905.9556/289.5836=13.5
Degrees of Freedom fornumerator = 2
Degrees of Freedom for denominator = 19
= 0.05
From Table, critical value of F =3.52
Since Calculated value of F =13.5 is greater than critical value of F = 3.52, the difference is significant. Reject null hypothesis.
Conclusion:
There are significant difference in the levels of IgG antibody across the groups. 