Cregg Hart is manufacturing manager for Larabee Engineering, a locomotive engine and rail car manufacturer. The company has been very successful in recent years, and in July 2016 signed two major contracts totaling nearly $200 million. A key to the company’s success has been its focus on quality. Customers from around the world have been very pleased with the attention to detail put forth by Larabee Engineering. One of the things Cregg has been adamant about is that Larabee Engineering’s suppliers also provide high quality. As a result, when the company finds good suppliers, it stays with them and tries to establish a long-term relationship. However, Cregg must also factor in the costs of parts and materials and has instructed his purchasing staff to be on the lookout for “better deals.” Recently, Sheryl Carleson, purchasing manager, identified a new rivet supplier in Europe that claims its rivets are as good or better quality than the current supplier’s but at a much lower cost. One key quality factor is the rivet diameter. When Sheryl approached Cregg about the possibility of going with the new supplier for rivets, he suggested they conduct a test to determine if there is any difference in the average diameter of the rivets from the two companies. Sheryl requested that the new company send 100 rivets, and she pulled a random sample of 100 rivets from her inventory of rivets from the original supplier. She then asked an intern to measure the diameters to three decimal places using a micrometer. The resulting data from both suppliers are given.:

Required Tasks:

Develop histograms showing the distribution of rivet diameters from the two suppliers.

Compute the sample means and standard deviations for the two sets of data.

Comment on whether it appears the assumptions required for testing if the two populations have equal mean diameters are satisfied.

Select a level of significance for testing whether the two suppliers have rivets with equal mean diameters. Discuss the factors you used in arriving at the level of significance you have selected.

Perform the appropriate null and alternative hypothesis test. Discuss the results.

Prepare a short report outlining your recommendation.

Sample Item Original Supplier New Supplier

1 0.374 0.391

2 0.387 0.375

3 0.359 0.365

4 0.391 0.36

5 0.39 0.366

6 0.361 0.378

7 0.376 0.377

8 0.371 0.364

9 0.373 0.332

10 0.364 0.343

11 0.39 0.378

12 0.384 0.401

13 0.384 0.382

14 0.383 0.381

15 0.381 0.363

16 0.369 0.371

17 0.361 0.352

18 0.376 0.393

19 0.382 0.359

20 0.368 0.367

21 0.354 0.371

22 0.366 0.328

23 0.359 0.37

24 0.394 0.374

25 0.365 0.387

26 0.39 0.374

27 0.378 0.394

28 0.398 0.342

29 0.366 0.373

30 0.376 0.384

31 0.366 0.356

32 0.392 0.366

33 0.373 0.374

34 0.374 0.34

35 0.375 0.347

36 0.363 0.418

37 0.38 0.359

38 0.398 0.36

39 0.382 0.343

40 0.362 0.384

41 0.362 0.389

42 0.379 0.358

43 0.379 0.386

44 0.369 0.365

45 0.384 0.382

46 0.366 0.359

47 0.376 0.389

48 0.381 0.364

49 0.381 0.389

50 0.373 0.387

51 0.385 0.37

52 0.378 0.361

53 0.392 0.391

54 0.372 0.385

55 0.362 0.382

56 0.371 0.374

57 0.388 0.365

58 0.377 0.337

59 0.384 0.414

60 0.368 0.403

61 0.362 0.397

62 0.372 0.39

63 0.359 0.418

64 0.395 0.374

65 0.37 0.369

66 0.391 0.394

67 0.358 0.375

68 0.376 0.38

69 0.369 0.342

70 0.385 0.372

71 0.398 0.386

72 0.365 0.361

73 0.379 0.352

74 0.397 0.406

75 0.37 0.393

76 0.384 0.391

77 0.368 0.391

78 0.374 0.365

79 0.364 0.391

80 0.376 0.353

81 0.364 0.375

82 0.372 0.362

83 0.381 0.388

84 0.382 0.38

85 0.368 0.398

86 0.375 0.384

87 0.371 0.366

88 0.361 0.393

89 0.374 0.385

90 0.39 0.388

91 0.376 0.419

92 0.374 0.358

93 0.387 0.339

94 0.371 0.384

95 0.36 0.357

96 0.386 0.363

97 0.377 0.437

98 0.365 0.38

99 0.374 0.378

100 0.363 0.369

Question

Cregg Hart is manufacturing manager for Larabee Engineering, a locomotive engine and rail car manufacturer. The company has been very successful in recent years, and in July 2016 signed two major contracts totaling nearly $200 million. A key to the company’s success has been its focus on quality. Customers from around the world have been very pleased with the attention to detail put forth by Larabee Engineering. One of the things Cregg has been adamant about is that Larabee Engineering’s suppliers also provide high quality. As a result, when the company finds good suppliers, it stays with them and tries to establish a long-term relationship. However, Cregg must also factor in the costs of parts and materials and has instructed his purchasing staff to be on the lookout for “better deals.” Recently, Sheryl Carleson, purchasing manager, identified a new rivet supplier in Europe that claims its rivets are as good or better quality than the current supplier’s but at a much lower cost. One key quality factor is the rivet diameter. When Sheryl approached Cregg about the possibility of going with the new supplier for rivets, he suggested they conduct a test to determine if there is any difference in the average diameter of the rivets from the two companies. Sheryl requested that the new company send 100 rivets, and she pulled a random sample of 100 rivets from her inventory of rivets from the original supplier. She then asked an intern to measure the diameters to three decimal places using a micrometer. The resulting data from both suppliers are given.:

Required Tasks:

Develop histograms showing the distribution of rivet diameters from the two suppliers.
Compute the sample means and standard deviations for the two sets of data.
Comment on whether it appears the assumptions required for testing if the two populations have equal mean diameters are satisfied.
Select a level of significance for testing whether the two suppliers have rivets with equal mean diameters. Discuss the factors you used in arriving at the level of significance you have selected.
Perform the appropriate null and alternative hypothesis test. Discuss the results.
Prepare a short report outlining your recommendation.

Sample Item	Original Supplier	New Supplier
1	0.374	0.391
2	0.387	0.375
3	0.359	0.365
4	0.391	0.36
5	0.39	0.366
6	0.361	0.378
7	0.376	0.377
8	0.371	0.364
9	0.373	0.332
10	0.364	0.343
11	0.39	0.378
12	0.384	0.401
13	0.384	0.382
14	0.383	0.381
15	0.381	0.363
16	0.369	0.371
17	0.361	0.352
18	0.376	0.393
19	0.382	0.359
20	0.368	0.367
21	0.354	0.371
22	0.366	0.328
23	0.359	0.37
24	0.394	0.374
25	0.365	0.387
26	0.39	0.374
27	0.378	0.394
28	0.398	0.342
29	0.366	0.373
30	0.376	0.384
31	0.366	0.356
32	0.392	0.366
33	0.373	0.374
34	0.374	0.34
35	0.375	0.347
36	0.363	0.418
37	0.38	0.359
38	0.398	0.36
39	0.382	0.343
40	0.362	0.384
41	0.362	0.389
42	0.379	0.358
43	0.379	0.386
44	0.369	0.365
45	0.384	0.382
46	0.366	0.359
47	0.376	0.389
48	0.381	0.364
49	0.381	0.389
50	0.373	0.387
51	0.385	0.37
52	0.378	0.361
53	0.392	0.391
54	0.372	0.385
55	0.362	0.382
56	0.371	0.374
57	0.388	0.365
58	0.377	0.337
59	0.384	0.414
60	0.368	0.403
61	0.362	0.397
62	0.372	0.39
63	0.359	0.418
64	0.395	0.374
65	0.37	0.369
66	0.391	0.394
67	0.358	0.375
68	0.376	0.38
69	0.369	0.342
70	0.385	0.372
71	0.398	0.386
72	0.365	0.361
73	0.379	0.352
74	0.397	0.406
75	0.37	0.393
76	0.384	0.391
77	0.368	0.391
78	0.374	0.365
79	0.364	0.391
80	0.376	0.353
81	0.364	0.375
82	0.372	0.362
83	0.381	0.388
84	0.382	0.38
85	0.368	0.398
86	0.375	0.384
87	0.371	0.366
88	0.361	0.393
89	0.374	0.385
90	0.39	0.388
91	0.376	0.419
92	0.374	0.358
93	0.387	0.339
94	0.371	0.384
95	0.36	0.357
96	0.386	0.363
97	0.377	0.437
98	0.365	0.38
99	0.374	0.378
100	0.363	0.369

Accepted Answer

The data of 100 samples of rivet diameter from both the suppliers :

Sample Item
Original…