A consulting firm advises on sampling and statistical procedures that can be used by their clients to control their manufacturing processes. A sample of a dimension existing 800 data points was collected from the process during a time that it was operating successfully. The sample standard deviation was .21 and since the number of samples was so large this was considered to be the population standard deviation. The consulting firm then suggested that data be collected in groups of 30 to periodically monitor and correct the process. The design specification was determined to be 12. The hypothesis test suggested by the consulting firm was: Ho: μ = 12 H1: μ ≠ 12
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A consulting firm advises on sampling and statistical procedures that can be used by their clients to control their manufacturing processes. A sample of a dimension existing 800 data points was collected from the process during a time that it was operating successfully. The sample standard deviation was .21 and since the number of samples was so large this was considered to be the population standard deviation. The consulting firm then suggested that data be collected in groups of 30 to periodically monitor and correct the process. The design specification was determined to be 12. The hypothesis test suggested by the consulting firm was:
Ho: μ = 12
H1: μ ≠ 12
Corrective action will be taken whenever Ho is rejected.
Sample 1 Sample 2 Sample 3
11.55 11.62 11.91
11.62 11.69 11.36
11.52 11.59 11.75
11.75 11.82 11.95
11.91 11.98 12.09
11.63 11.70 11.72
11.81 11.86 11.60
12.02 12.10 11.85
11.94 12.01 12.66
11.91 12.01 12.17
12.17 12.19 12.13
12.11 12.21 12.14
11.93 12.01 12.22
12.22 12.29 11.56
12.31 12.41 11.95
11.93 12.04 12.02
11.85 11.93 11.74
11.76 11.83 11.76
12.16 12.24 11.83
11.77 11.85 12.14
12.00 12.37 11.60
12.04 12.12 11.95
11.98 12.05 11.96
12.30 12.37 12.22
12.18 12.25 11.83
11.97 12.05 11.98
12.17 12.25 11.91
11.85 11.91 11.89
12.30 12.37 11.88
12.15 12.22 11.93
- What is the standard deviation for each of the three samples? Does the assumption of .21 for the population standard deviation appear reasonable?
- Compute a new sample
mean that includes all three samples such that as long as the new sample mean is within the lower and upper levels the process is considered to be operating satisfactorily. - What are the implications if the level of significance is decreased to a lower value, say .005?
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