Question

Two quality control technicians measured the surface finish of a metal part, obtaining the data shown. Assume that the measurements are normally distributed. Use Minitab© for all tests and calculations.

Tech 1	1.45	1.37	1.21	1.54	1.48	1.29	1.34	*
Tech 2	1.54	1.41	1.56	1.37	1.20	1.31	1.27	1.35

a) Does the normality assumption seem reasonable for the data? Are the variances equal? How do you know?

b) The supervisor asks you to test the hypothesis that the difference in the mean surface finish measurements made by the two technicians is equal to zero. Use α = 0.05 and assume equal variances.

c) He then asks to test the hypothesis that the variances of the measurements made by the two technicians are equal. Use α = 0.05. What can be inferred if the null hypothesis is rejected?

d) What are the practical implications of the test in part (b)? Discuss what practical conclusions you would draw if the null hypothesis were rejected.

e) Explain your findings to your supervisor.

Answer 1

a) Testing the normality assumption for variable Tech 1,

Using Minitab software, (Stat -> Basic Statistics -> Normality Test), we get the following output -

Since P-value > 0.05, so at 5% level of significance, we can conclude that Tech 1 variable is normal.

Testing the normality assumption for variable Tech 2,

Since P-value > 0.05, so at 5% level of significance, we can conclude that Tech 2 variable is normal.

b) Testing the hypothesis that the difference in the mean surface finish measurements made by the two technicians is equal to zero,

i.e. to test against

Using Minitab software, (Stat -> Basic Statistics -> 2 sample t), we get the following output -

Here,

The value of the test statistic t = 0.11

and P-value = 0.917

Since P-value > 0.05, so at 5% level of significance, we fail to reject H₀ and we can conclude that the difference in the mean surface finish measurements made by the two technicians is not significantly different from 0.

c) Testing the the hypothesis that the variances of the measurements made by the two technicians are equal,

i.e. to test against

Using Minitab software, (Stat -> Basic Statistics -> 2 sample t), we get the following output -

Since P-value > 0.05, so at 5% level of significance, we fail to reject H₀ and we can conclude that the variances of the measurements made by the two technicians are not significantly different.