Question

A new production process is being contemplated for the manufacture of stainless steel bearings. Measurements of the diameters of random samples of bearings from the old and new processes produced the following data (all in mm): Old

Old	New
16.3	15.9
15.9	16.2
15.8	16.0
16.2	15.8
16.1	16.1
16.0	16.1
15.7	15.8
15.8	16.0
15.9	16.2
16.1	15.9
16.3	15.7
16.1	16.2
15.8	15.8
15.7	15.8
15.8	16.2
15.7	16.3

.

A. Can you conclude that the variances between the new and old procedure are different? Use formal hypothesis testing.

b. Can you conclude that there is a difference in mean diameter between the procedures? Use formal hypothesis testing.

c. Management wants to know if the new procedure is comparable to the old procedure. What can you tell them? (Give a yes/no answer and your reasoning, based on statistics.)

Answer 1

We use Minitab to solve this question-

A) No, We can not conclude that the variances between the new and old procedure are different because,
P-value = 0.703 > 0.05 therefore we do not reject the null hypothesis of equality of variance.

B) From part A we conclude that variances of both procedures are not different therefore we use pooled t test.

   No, We can not there is a difference in mean diameter between the procedures because,
P-value = 0.485 > 0.05 therefore we do not reject the null hypothesis of equality of means of two procedures.

C) No, new procedure is not comparable to the old procedure because in part-B we fail to reject hypothesis of equality of means of two procedures.