Question

A maintenance manager for an injection molding area must test a new repair method that is expected to increase the time between repairs. She uses the methods in 10 different machines. She repairs the machine with each method and then records the time (hrs) that the machine takes to become damaged again. Presume that times are normal.

Machine	1	2	3	4	5	6	7	8	9	10
Old	150	225	345	287	115	390	200	450	440	250
New	210	345	420	277	245	420	310	505	395	210

Conduct the test of appropriate hypothesis using a 5% level of significance. What would be your recommendation?

Answer 1

Let us denote

d : difference in time between repair time in old and new repair method

To test whether new repair method increases the time between repairs,

i.e.   against

Here

sample mean of diiference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if

Now,

The value of the test statistic

and critical value

Since , we reject H₀ at 5% level of significance and we can conclude that new repair method significantly increases the time between repairs.