An aircraft manufacturer needs to buy aluminum sheets with an average thickness of 0.05 inch. The manufacturer knows that significantly thinner sheets would be unsafe and considerably thicker sheets would be too heavy. A random sample of 100 sheets from a potential supplier is collected.

a. Use the p-value approach to determine if the aircraft manufacturer should buy aluminum sheets from the supplier.

b. For which values of the sample mean would the aircraft manufacturer decide to buy sheets from this supplier, assuming α = 0.05?

Please, show your work.

Sheet	Thickness
1	0.0403
2	0.0693
3	0.0632
4	0.0651
5	0.0534
6	0.0574
7	0.0400
8	0.0515
9	0.0542
10	0.0555
11	0.0512
12	0.0525
13	0.0434
14	0.0392
15	0.0607
16	0.0575
17	0.0637
18	0.0358
19	0.0455
20	0.0319
21	0.0578
22	0.0488
23	0.0402
24	0.0318
25	0.0447
26	0.0306
27	0.0325
28	0.0542
29	0.0416
30	0.0517
31	0.0448
32	0.0520
33	0.0495
34	0.0525
35	0.0618
36	0.0571
37	0.0391
38	0.0655
39	0.0568
40	0.0370
41	0.0505
42	0.0425
43	0.0611
44	0.0491
45	0.0574
46	0.0603
47	0.0420
48	0.0616
49	0.0463
50	0.0340
51	0.0609
52	0.0457
53	0.0409
54	0.0367
55	0.0713
56	0.0576
57	0.0515
58	0.0549
59	0.0325
60	0.0470
61	0.0203
62	0.0379
63	0.0442
64	0.0384
65	0.0409
66	0.0358
67	0.0442
68	0.0538
69	0.0486
70	0.0317
71	0.0529
72	0.0449
73	0.0437
74	0.0384
75	0.0400
76	0.0397
77	0.0486
78	0.0296
79	0.0548
80	0.0407
81	0.0552
82	0.0412
83	0.0425
84	0.0371
85	0.0590
86	0.0398
87	0.0600
88	0.0589
89	0.0496
90	0.0509
91	0.0427
92	0.0481
93	0.0512
94	0.0504
95	0.0467
96	0.0253
97	0.0195
98	0.0471
99	0.0464
100	0.0529