George received a complaint from a customer that a critical part diameter may be out of specification on the most profitable assembly in the plant. The diameter specification is 0.5

0.010 inch. For this process, only five assemblies are produced per day, and you need twenty samples. You task your quality team to collect diameter data for the five samples per day for the next twenty days. The data is recorded as deviations from the nominal half inch measurement and recorded in thousandths of an inch.

George also asked you to determine if a new process is in statistical control, and you need to establish a center line and control limits for np charts with sample sizes of n=500 parts per day. You have been running the new process for the past 10 days and the number of nonconforming

parts per day is recorded below. Be sure to address how you will investigate assignable causes and adjust your control limits based on your findings.

Use descriptive statistics and inferential statistics to address George's project to gain insight on the customer's complaint. Test the hypothesis that the critical part is out of spec. Describe how control charts are related to hypothesis testing. Extend your explanation further using George's new process.

Day	Number nonconforming parts
1	2
2	4
3	3
4	2
5	6
6	12
7	5
8	1
9	2
10	2

sample #	x1	x2	x3	x4	x5
1	-3	5	-2	1	3
2	0	5	-6	-2	3
3	-5	1	2	3	2
4	-1	-1	3	-2	5
5	2	-4	5	2	1
6	0	0	4	-4	2
7	0	0	2	-2	-1
8	7	-3	3	-1	0
9	0	0	2	-2	1
10	1	2	3	1	5
11	4	0	2	0	2
12	13	12	13	11	14
13	3	-3	0	1	1
14	3	-1	5	-1	-3
15	1	-1	5	4	0
16	0	0	3	-1	0
17	2	2	3	3	-2
18	1	-2	5	3	1
19	5	-1	4	2	0
20	5	0	0	3	1