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

H₀: =12

H_a: 12

Corrective action will be taken any time H₀ is rejected.

The samples on the following page were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data are available on the DATAfile named Quality.

Managerial Report:

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

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

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

Please explain in detail by detail on how you got the answers. I badly need to understand this. I hope you understand. Thank you.