Question

Quality Improvement Partners (QIP) is a consulting firm that advises clients about sampling and statistical procedures that can be used to control their manufacturing processes. Your company has given QIP a sample of 800 observations taken during a time in which your process was operating satisfactorily.

The design specification indicates the mean measurement for the process should be 12. The sample standard deviation for these data was 0.21. With that much data, you can assume the population standard deviation is 0.21.

QIP has suggested that periodic random samples of size 30 be taken so you can monitor the process on an ongoing basis. By analyzing the new samples, you can quickly learn whether the process is operating satisfactorily or if it is operating differently than the expected mean. When the process is not operating satisfactorily, corrective action can be taken to attempt to eliminate the root cause(s) (assuming you know what they are). You will take corrective action whenever you reject the null hypothesis at the 0.01 significance level. Use this information to answer the questions in this Data Lab.

Sample 1	Sample 2	Sample 3	Sample 4
11.55	11.62	11.91	12.02
11.62	11.96	11.36	12.02
11.52	11.59	11.75	12.05
11.75	11.82	11.95	12.18
11.9	11.97	12.14	12.11
11.64	11.71	11.72	12.07
11.8	11.87	11.61	12.05
12.03	12.1	11.85	11.64
11.94	12.01	12.16	12.39
11.92	11.99	11.91	11.65
12.13	12.2	12.12	12.11
12.09	12.16	11.61	11.9
11.93	12	12.21	12.22
12.21	12.28	11.56	11.88
12.32	12.39	11.95	12.03
11.93	12	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	12.2
11.77	11.84	12.12	11.79
12	12.07	11.6	12.3
12.04	12.11	11.95	12.27
11.98	12.05	11.96	12.29
12.3	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
12.3	12.37	11.88	12.23
12.15	12.22	11.93	12.25

1. Run the appropriate hypothesis test and record the test-statistics (z or t) for each of the samples.

Sample 1:  (Round to 4 decimal places)

Sample 2:  (Round to 4 decimal places)

Sample 3:  (Round to 4 decimal places)

Sample 4:  (Round to 4 decimal places)

2.  Run the appropriate hypothesis test and record the p-values for each sample

Sample 1:  (Round to 4 decimal places)

Sample 2:  (Round to 4 decimal places)

Sample 3:  (Round to 4 decimal places)

Sample 4:  (Round to 4 decimal places)

Answer 1

1.

Sample 1:  -1.0781

Sample 2:  0.9824

Sample 3: -2.8951

Sample 4:  2.1213

2.

Sample 1:  0.2810

Sample 2:  0.3259

Sample 3:  0.0038

Sample 4:  0.0339

The output is:

12.000000	hypothesized value	12.000000	hypothesized value	12.00000	hypothesized value	12.000000	hypothesized value
11.958667	mean Sample 1	12.037667	mean Sample 2	11.88900	mean Sample 3	12.081333	mean Sample 4
0.210000	std. dev.	0.210000	std. dev.	0.21000	std. dev.	0.210000	std. dev.
0.038341	std. error	0.038341	std. error	0.03834	std. error	0.038341	std. error
30	n	30	n	30	n	30	n
-1.0781	z	0.9824	z	-2.8951	z	2.1213	z
0.2810	p-value (two-tailed)	0.3259	p-value (two-tailed)	0.0038	p-value (two-tailed)	0.0339	p-value (two-tailed)

The data is:

Sample 1	Sample 2	Sample 3	Sample 4
11.55	11.62	11.91	12.02
11.62	11.96	11.36	12.02
11.52	11.59	11.75	12.05
11.75	11.82	11.95	12.18
11.9	11.97	12.14	12.11
11.64	11.71	11.72	12.07
11.8	11.87	11.61	12.05
12.03	12.1	11.85	11.64
11.94	12.01	12.16	12.39
11.92	11.99	11.91	11.65
12.13	12.2	12.12	12.11
12.09	12.16	11.61	11.9
11.93	12	12.21	12.22
12.21	12.28	11.56	11.88
12.32	12.39	11.95	12.03
11.93	12	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	12.2
11.77	11.84	12.12	11.79
12	12.07	11.6	12.3
12.04	12.11	11.95	12.27
11.98	12.05	11.96	12.29
12.3	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
12.3	12.37	11.88	12.23
12.15	12.22	11.93	12.25

Please give me a thumbs-up if this helps you out. Thank you!