Was the draft lottery random

Question

Discuss the following:

Q1 Refer to excel file for data

Was the draft lottery random?

In 1970, a lottery was used to determine who would be drafted into the US Army. The 366 dates in the year were placed in individual capsules. First the 31 January capsules were placed in a box: then the 29 February capsules were added and the two months were mixed.

Then the 31 March capsules were added and the three months were mixed. This process continued until all months were included. The first capsule selected was September 14, so men born on that date were drafted first. The accompanying list show the 366 dates in the order of selection.

a- Use the runs test to test the sequence for randomness above and below the median of 183.5

b- Use the Kruskal-Wallis test to test the claim that the 12 months had priority numbers drawn from the same population.

c- Calculate the 12 monthly means. Then plot those 12 means on a graph. (The horizontal scale lists the 12 months and the vertical scale ranges from 100 to 260). Note any pattern suggesting that the original priority numbers were not randomly selected.

d- Based on the results from arts (a), (b) and (c), decide whether this particular draft lottery was fair. Write a statement either supporting your position that it was fair or explaining why you believe that it was not fair. If you decided that this lottery was unfair, describe a process for selecting lottery numbers that would be fair.

Q2 Refer to excel file for data

Are the axial loads within statistical control? Is the process of manufacturing cans proceeding as it should?
New York Company manufactures 0.0109-in. thick aluminum cans for a major beverage supplier.

From the data conduct an analysis of the process data for the cans that are 0.0111 in. think. The values in the data a set are measured axial loads of cans, and the top lids are pressed into place with pressures that vary between 158 lb and 165 lb.

Analyzing the results:

Based on the given process data, should the company take any corrective actions? Write a report summarizing your conclusions. Address not only the issue of statistical stability, but also the ability of the cans to withstand the pressures applied when the top lids are pressed into place. Also compare the behavior of the 0.0111-in. cans to the behavior of the 0.0109 in. cans and recommend which thickness should be used?

251	215	101	224	306	199	194	325	329	221	318	238	17	121
58	280	186	337	118	59	52	92	355	77	349	164	211
297	210	214	347	91	181	338	216	150	68	152	4	89	212
25	302	363	290	57	236	179	365	205	299	285
267	275	293	139	122	213	317	323	136	300	259	354	169	166
200	239	334	265	256	258	343	170	268	223	362	217	30
83	81	269	253	147	312	219	218	14	346	124	231	273	148
336	345	62	316	252	2	351	340	74	262	191	208
40	276	364	155	35	321	197	65	37	133	295	178	130	55
75	183	250	326	319	31	361	357	296	308	226	103	313
301	20	28	110	85	366	335	206	134	272	69	356	180	274
104	360	60	247	109	358	137	22	64	222	353	209
115	279	188	327	50	13	277	284	248	15	42	331	322	120
227	187	27	153	172	23	67	303	289	88	270	287	193
261	145	54	114	168	48	106	21	324	142	307	198	102	44
311	344	291	339	116	36	286	245	352	167	61	333	11
49	232	82	6	8	184	263	71	158	242	175	1	113	207
177	63	204	160	119	195	149	18	233	257	151	315
244	302	24	87	234	283	342	220	237	72	138	294	171	254
241	192	243	117	201	196	176	7	264	94	229	38	79
348	266	310	76	51	97	80	282	46	66	126	127	131	107
203	182	156	9	182	230	132	309	47	281	99	174
157	165	56	10	12	105	43	41	39	314	163	26	320	96
240	135	70	53	162	95	84	173	78	123	16	3	100