The variability in measurements made by two devices is studi

The variability in measurements made by two devices is studied. During the comparison test, the following measurements were obtained by using device 1: and device 2 yielded the following results: Perform analysis concerning equality of the measurement variances of the devices. (Use the table at 5% significant level)

Solution

Assuming the measurments are made of the same population by two different instruments, the question is the compare the variances of the two measurments and determine if the instruments are within the normal 95% range permissible by random error.

The use this analyse the measurements by a t-test

Data from instrument 1 give mean 13.69, variance 3.263, n=10

Data from instrument 2 give mean 1.696, variance 1.3585, n=8

s^2 = [ ( 10-1)* s1*s1 + (n2-1) *s2*s2]/ ( n1-a +n2-1) = 6.79645

s (composite) = 2.607

t value = ( mean 1-mean2)/[s( 1/n1 +1/n2)]

t = (16.4625-13.69)/s*sqrt(.1+.125) = 2.242

From Tables: or using EXCEL with either homoscedastic or unequal variance

the results are almost same and less than 5%

18.9 18.9 17.8 16.8 11.7 17.6 10.1 16.1 12.2 14.4 13.3 15.6 15.9 15.8 16 16.5 9.5 0.030576 11.5 0.039487