Question

A production manager is interested in comparing the precision of two brands of stamping machines. From a random sample of 12 units of output from the Brand A machine, a standard
deviation of 15.2 is reported for a quality characteristic. For the Brand B machine, in a
sample of 20 units of output, there is a standard deviation of 10.1. Is there sufficient evidence
at the 5% significance level to conclude that Brand B machines have a lower variance in
quality? Assume that the quality characteristic of both machines follows a normal
distribution.

Answer 1

For machine A, standard deviation s1 = 15.2 and sample size n1 =12

For machine B, standard deviation s1 = 10.1 and sample size n1 =20

Null hypothesis

Alternate hypothesis

test statistic

degree of freedom (df1) = n1 - 1 = 12-1 = 11

degree of freedom (df2) = n2 - 1 = 20-1 = 19

using excel function F.DIST.RT(x,df1,df2) where x = 2.265, df1 =11 and df2 = 19

p-value = F.DIST.RT(2.265,11,19) =0.0567

here, p-value(0.0567) > significance level (0.05), failing to reject the null hypothesis

Conclusion:- there is insufficient evidence to conclude that Brand B machines have a lower variance in
quality