Question

Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturingprocesses. IN one particular application, a client game quality associates a sample of 800 observations taken during a time in which that client's process wasoperating satisfactorily. The sample standard deviation for there data was .21 ; hence, with so much data, the population standard deviation was assumed to be .21.Quality associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. BY analyzing the new samples,the client could quickly learn whether the process was operating satisfactorily. when the process was not operating satisfactorily, corrective action could be taketo eliminate the problem. the design specification indicated the mean for the process should be 12. the hypothesis test suggested Quality Associates follows.

: μ=12
: μ12

Corrective action will be take any time H0 is rejected.

The following samples were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data areavailable in the data set Quality .

Sample 1	Sample 2	Sample 3	Sample 4
11.55	11.62	11.91	12.02
11.62	11.69	11.36	12.02
11.52	11.59	11.75	12.05
11.75	11.82	11.95	12.18
11.90	11.97	12.14	12.11
11.64	11.71	11.72	12.07
11.80	11.87	11.61	12.05
12.03	12.10	11.85	11.64
11.94	12.01	12.16	12.39
11.92	11.99	11.91	11.65
12.13	12.20	12.12	12.11
12.09	12.16	11.61	11.90
11.93	12.00	12.21	12.22
12.21	12.28	11.56	11.88
12.32	12.39	11.95	12.03
11.93	12.00	12.01	12.35
11.85	11.92	12.06	12.09
11.76	11.83	11.76	11.77
12.16	12.23	11.82	12.20
11.77	11.84	12.12	11.79
12.00	12.07	11.60	12.30
12.04	12.11	11.95	12.27
11.98	12.05	11.96	12.29
12.30	12.37	12.22	12.47
12.18	12.25	11.75	12.03
11.97	12.04	11.96	12.17
12.17	12.24	11.95	11.94
11.85	11.92	11.89	11.97
12.30	12.37	11.99	12.23
12.15	12.22	11.93	12.25

Managerial Report:

1) Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any, should be take. Provide the test statistic andp-value for each test.

2) Compute the standard deviation for each of the four samples. Does the assumption of .21 for the population standard deviation appear reasonable?

3) Compute limits for the sample mean X around μ=12 such that, as long as a new sample mean is within those limits, the process will be considered to beoperating satifactorily. If X exceeds the upper limit or if X is below the lower limit, corrective action will be taken. These limits are refferred to as upper andlower control limits fro quality control purposes.

4) Discuss the implications of changing the level of significance to a larger value. What mistakes or error could increase if the level of significance inincreased?

Answer 1

Yes .Since the sample standation values nearer to the assumption of 0.21 for the population standard deviation .So it is appear reasonable.

From the above out put for sample 3,4,5 to Conduct a hypothesis test for each sample at the .01 level of significance we have the followingconclusions.Sample2Since p-value=0.482>0.01 we fail to reject H0Sample3Since p-value=0.006<0.01 we reject H0Sample4Since p-value=0.039>0.01 we fail to reject H0

Suppose α=0.01 is incresed to 0.05 then the implications of changing the level of significance to a larger valueif α = type 1error could increase then the level of significance in increased a larger value.