chapter 9
Peter j. Dalley, The case study has given to us is regarding Quality Associates, Inc. It’s a consulting firm. Quality Associates, Inc. advises its clients about sampling and statistical procedures. In this particular case, Quality Associates, Inc. has provided samples to be analyzed, so it’s client can quickly learn whether the process is operating satisfactorily or corrective actions needs to be taken.
Summary of Statistics
Sample 1 Sample 2 Sample 3 Sample 4
Mean
11.96
12.10
12.14
12.15
Standard Error
0.04
0.04
0.04
0.02
Standard Deviation
0.22
0.23
0.23
0.16
Sample Variance
0.05
0.05
0.05
0.03
Sum
358.69
362.90
364.08
364.46
From the summary of statistics we can see that mean has an upward trend. Mean value differ from sample to sample. Here we can observe that mean value has a relation with the amount of sum. We can also notice that amount of sum is differing from sample to sample and follow the same trend as mean.
Introduction of the test: By analyzing the new samples, the client would be able to know that, whether the process was operating satisfactorily or not. If the process was not operating satisfactorily, then corrective action would be taken to eliminate the problem. In this case the mean for the process is 12. The hypothesis test suggested by Quality Associates follows:
H0: μ=12
Ha: μ≠ 12
Corrective action will be taken if H0 is rejected. In this case α = .01 that means probability of making a Type I error when μ = 12 is .01.
Sample 1
Sample 2
Sample 3
Sample 4
Z statistics
-1.14
2.52
3.55
3.88
P value
0.26
0.01
0.00
0.00
Accept
Reject
Reject
Reject
Here we can see in Sample 1, P-value is higher than α. So sample 1 is operating satisfactorily, so in case of sample 1 we are going to accept null and no corrective
Summary of Statistics
Sample 1 Sample 2 Sample 3 Sample 4
Mean
11.96
12.10
12.14
12.15
Standard Error
0.04
0.04
0.04
0.02
Standard Deviation
0.22
0.23
0.23
0.16
Sample Variance
0.05
0.05
0.05
0.03
Sum
358.69
362.90
364.08
364.46
From the summary of statistics we can see that mean has an upward trend. Mean value differ from sample to sample. Here we can observe that mean value has a relation with the amount of sum. We can also notice that amount of sum is differing from sample to sample and follow the same trend as mean.
Introduction of the test: By analyzing the new samples, the client would be able to know that, whether the process was operating satisfactorily or not. If the process was not operating satisfactorily, then corrective action would be taken to eliminate the problem. In this case the mean for the process is 12. The hypothesis test suggested by Quality Associates follows:
H0: μ=12
Ha: μ≠ 12
Corrective action will be taken if H0 is rejected. In this case α = .01 that means probability of making a Type I error when μ = 12 is .01.
Sample 1
Sample 2
Sample 3
Sample 4
Z statistics
-1.14
2.52
3.55
3.88
P value
0.26
0.01
0.00
0.00
Accept
Reject
Reject
Reject
Here we can see in Sample 1, P-value is higher than α. So sample 1 is operating satisfactorily, so in case of sample 1 we are going to accept null and no corrective