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 pop
- 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
a) Conduct a hypothesis test for each of the three samples at the .01 level of significance. What action, if any, should be taken? Provide the test statistic and p-value for each test.
b) What is the standard deviation for each of the three samples? Does the assumption of .21 for the population standard deviation appear reasonable?
c) Compute a new sample
d) What are the implications if the level of significance is decreased to a lower value, say .005?
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