F-test Predict if the precision levels of two methods given in numerical above differ significantly or not. Given. F6.39 atv, 4 at 95% confidence level Entymatic method ()
13.1 12.7 12.6 13.3 13.3
DC method()13.5 13.3
13.0
12.9
13.0
To determine if the precision levels of the two methods differ significantly, we can perform an F-test using the given data.
First, we calculate the sample means for each method:
Entymatic method:
Mean = (13.1 + 12.7 + 12.6 + 13.3 + 13.3) / 5 = 12.8
DC method:
Mean = (13.5 + 13.3 + 13.0 + 12.9 + 13.0) / 5 = 13.14
Next, we calculate the sum of squares of deviations from the mean for each method:
Entymatic method:
SS = (13.1 - 12.8)^2 + (12.7 - 12.8)^2 + (12.6 - 12.8)^2 + (13.3 - 12.8)^2 + (13.3 - 12.8)^2 = 0.33
DC method:
SS = (13.5 - 13.14)^2 + (13.3 - 13.14)^2 + (13.0 - 13.14)^2 + (12.9 - 13.14)^2 + (13.0 - 13.14)^2 = 0.90
Now, we calculate the F-statistic using the formula:
F = (SS of the DC method / degrees of freedom of DC method) / (SS of the Entymatic method / degrees of freedom of the Entymatic method)
Degrees of freedom for both methods is 4.
F = (0.90 / 4) / (0.33 / 4) = 2.73
Using a critical F-value of 6.39 at a 95% confidence level with degrees of freedom 4 and 4, we can see that the calculated F-value of 2.73 is less than the critical value. Therefore, we can conclude that there is no significant difference in the precision levels of the two methods.