irst, analyze the relationship between company and hub by calculating simple and conditional probabilities: (a) P(DWN): (b) P(NatEx): (c) P(Chicago): (d) P(Denver): (e) P(Chicago|Natex): (f) P(Denver|Natex): (g) P(Chicago|DWN): (h) P(Denver|DWN): (i) P(Natex|Chicago): (j) P(Natex|Denver): (k) P(DWN|Chicago): (l) P(DWN|Denver): 2. Note that NatEx is more likely to ship out of Chicago, and DWN is more likely to ship out of Denver. From earlier in the semester, you would conclude that company and hub were statistically dependent, since, for example, P(Chicago|Natex) = .6842, and P(Chicago)= .60. Since they are not equal, then they are dependent. But the question now is whether that difference is statistically significant, or whether it is just chance sampling error. Now conduct a chi-square test: (a) chi-square test statistic: (b) P-value: (c) conclusion: 3. Now examine the relationship between company and delivery: (a) P(late): (b) P(late|DWN): (c) P(late|NatEx): 4. Since P(late) 6 = P(late|DXN) (or P(late) 6 = P(late|NatEx), you would earlier in the semester have concluded that company and delivery are dependent events. But is the difference just chance sampling error?

company	hub	delivery	weight	distance	price
DWN	Chicago	ontime	78.4	246	3.27
DWN	Chicago	late	65.8	314	2.9
DWN	Chicago	ontime	68.8	201	2.5
DWN	Chicago	ontime	69.6	489	4.15
DWN	Chicago	late	85.4	351	4.85
DWN	Chicago	late	87.3	300	4.24
DWN	Chicago	late	87.5	301	3.77
DWN	Chicago	late	89	342	4.24
DWN	Chicago	late	89.3	349	4.59
DWN	Chicago	late	95.2	366	5.1
DWN	Chicago	late	95.6	360	4.02
DWN	Chicago	ontime	97.6	249	4.42
DWN	Chicago	late	98.2	123	3.24
DWN	Chicago	late	98.7	431	5.13
DWN	Chicago	late	107.8	492	5.61
DWN	Chicago	late	108.3	383	5.52
DWN	Chicago	late	110.3	445	6.2
DWN	Chicago	late	110.7	371	6.01
DWN	Chicago	late	112.7	230	4.99
DWN	Chicago	ontime	135	395	5.74
DWN	Denver	late	62.1	167	1.91
DWN	Denver	ontime	66	394	3.69
DWN	Denver	ontime	71.6	54	1.7
DWN	Denver	late	73	348	3.55
DWN	Denver	ontime	75	185	2.61
DWN	Denver	ontime	77.2	210	2.32
DWN	Denver	ontime	80.8	152	3.58
DWN	Denver	ontime	81.6	443	3.84
DWN	Denver	ontime	81.9	277	3.89
DWN	Denver	ontime	82	166	2.84
DWN	Denver	ontime	82.9	444	4.57
DWN	Denver	ontime	84.1	438	3.98
DWN	Denver	ontime	66.5	361	4.13
DWN	Denver	ontime	68.3	308	3.77
DWN	Denver	ontime	73	272	3.03
DWN	Denver	ontime	73	360	4.47
DWN	Denver	ontime	76.8	359	4.03
DWN	Denver	ontime	80.2	307	5.11
DWN	Denver	ontime	83.2	176	3.65
DWN	Denver	ontime	89.2	625	5.73
DWN	Denver	late	89.8	358	4.15
DWN	Denver	late	91.2	371	4.71
DWN	Denver	ontime	93.8	543	5.99
DWN	Denver	ontime	94	297	4.36
DWN	Denver	late	94.7	228	4.59
DWN	Denver	late	97.2	427	6.07
DWN	Denver	late	97.9	463	6.25
DWN	Denver	ontime	98.7	483	5.39
DWN	Denver	ontime	100.5	476	5.02
DWN	Denver	late	100.6	523	5.5
DWN	Denver	late	106.5	557	6.43
DWN	Denver	late	108.4	594	6.8
DWN	Denver	ontime	108.6	444	5.69
DWN	Denver	ontime	113.5	462	5.02
DWN	Denver	late	114.3	346	5.16
DWN	Denver	ontime	115.1	665	6.37
DWN	Denver	late	115.5	349	5.4
DWN	Denver	ontime	115.6	392	6.22
DWN	Denver	late	127.7	577	7.2
DWN	Denver	ontime	133.5	447	6.44
NatEx	Chicago	late	56.8	223	1.92
NatEx	Chicago	ontime	63	68	0.85
NatEx	Chicago	ontime	68.2	287	3.44
NatEx	Chicago	ontime	70.2	123	2.69
NatEx	Chicago	ontime	71.5	276	2.75
NatEx	Chicago	late	73.1	318	3.39
NatEx	Chicago	late	77.5	270	3.63
NatEx	Chicago	ontime	77.7	393	3.2
NatEx	Chicago	ontime	78	243	2.48
NatEx	Chicago	ontime	78.3	169	3.24
NatEx	Chicago	ontime	78.5	319	2.83
NatEx	Chicago	ontime	84.3	166	2.68
NatEx	Chicago	late	84.6	263	3.28
NatEx	Chicago	late	65.2	387	3.99
NatEx	Chicago	ontime	68	455	4.13
NatEx	Chicago	late	68.7	227	3.07
NatEx	Chicago	ontime	68.8	403	4.48
NatEx	Chicago	ontime	69.1	314	3.22
NatEx	Chicago	late	69.3	387	3.43
NatEx	Chicago	late	70.3	416	3.72
NatEx	Chicago	ontime	70.3	149	3.61
NatEx	Chicago	ontime	70.5	264	3.38
NatEx	Chicago	ontime	70.8	368	4.15
NatEx	Chicago	late	71.2	205	3.42
NatEx	Chicago	late	71.6	326	4.09
NatEx	Chicago	ontime	71.7	290	4.42
NatEx	Chicago	ontime	72.9	319	4.4
NatEx	Chicago	ontime	73	247	3.67
NatEx	Chicago	ontime	73.8	272	3.77
NatEx	Chicago	late	74.2	510	4.21
NatEx	Chicago	late	75.2	275	3.76
NatEx	Chicago	late	75.7	336	4.11
NatEx	Chicago	late	76.1	172	2.82
NatEx	Chicago	ontime	76.3	363	4.7
NatEx	Chicago	ontime	76.5	411	4.14
NatEx	Chicago	late	76.7	306	3.94
NatEx	Chicago	ontime	76.8	465	5
NatEx	Chicago	ontime	78.8	299	3.88
NatEx	Chicago	ontime	79.4	272	3.48
NatEx	Chicago	late	80.2	217	3.36
NatEx	Chicago	late	80.2	157	3.28
NatEx	Chicago	ontime	80.3	659	5.13
NatEx	Chicago	late	81.1	330	4.39
NatEx	Chicago	late	81.5	463	4.67
NatEx	Chicago	late	81.7	429	4.09
NatEx	Chicago	late	82.4	485	4.39
NatEx	Chicago	late	82.8	299	3.72
NatEx	Chicago	ontime	83	250	3.26
NatEx	Chicago	ontime	84	289	3.86
NatEx	Chicago	ontime	84.8	244	3.38
NatEx	Chicago	ontime	85.1	347	4.39
NatEx	Chicago	late	85.9	520	5.46
NatEx	Chicago	late	86.6	396	5.04
NatEx	Chicago	late	86.8	395	4.58
NatEx	Chicago	late	87.7	159	2.92
NatEx	Chicago	late	87.8	251	4.57
NatEx	Chicago	late	87.8	463	4.19
NatEx	Chicago	ontime	88.4	415	4.1
NatEx	Chicago	ontime	88.4	572	5.98
NatEx	Chicago	late	88.7	520	5.72
NatEx	Chicago	late	89.2	299	4.07
NatEx	Chicago	late	89.4	75	3.1
NatEx	Chicago	late	89.9	358	4.62
NatEx	Chicago	late	89.9	316	4.66
NatEx	Chicago	ontime	90.7	471	5.41
NatEx	Chicago	late	90.7	443	5.48
NatEx	Chicago	late	90.8	358	3.85
NatEx	Chicago	late	91.1	317	4.22
NatEx	Chicago	late	92.7	145	3.61
NatEx	Chicago	late	93.3	319	4.71
NatEx	Chicago	late	93.8	316	4.13
NatEx	Chicago	late	94.4	426	5.39
NatEx	Chicago	late	94.7	542	5.31
NatEx	Chicago	late	94.8	245	4.12
NatEx	Chicago	late	94.8	201	3.79
NatEx	Chicago	ontime	95.2	393	4.78
NatEx	Chicago	late	95.3	328	4.9
NatEx	Chicago	late	96.7	335	3.95
NatEx	Chicago	late	96.7	74	3.41
NatEx	Chicago	late	97.7	328	4.3
NatEx	Chicago	late	97.8	345	5.14
NatEx	Chicago	late	98.6	473	5.67
NatEx	Chicago	late	98.7	415	4.93
NatEx	Chicago	late	98.8	458	4.73
NatEx	Chicago	late	100.3	563	5.63
NatEx	Chicago	late	100.4	301	4.9
NatEx	Chicago	late	100.6	468	4.98
NatEx	Chicago	ontime	100.9	331	4.76
NatEx	Chicago	late	101.1	446	5.37
NatEx	Chicago	ontime	101.3	433	4.85
NatEx	Chicago	ontime	101.4	249	4.35
NatEx	Chicago	late	101.6	370	5.31
NatEx	Chicago	ontime	101.8	433	5.24
NatEx	Chicago	ontime	102	425	5.33
NatEx	Chicago	late	102.9	454	5.23
NatEx	Chicago	late	102.9	363	4.11
NatEx	Chicago	ontime	104.7	259	4.74
NatEx	Chicago	late	105.5	375	5.05
NatEx	Chicago	late	106.4	450	5.72
NatEx	Chicago	late	106.6	270	5.08
NatEx	Chicago	late	106.6	362	4.29
NatEx	Chicago	late	108.5	307	4.85
NatEx	Chicago	late	111.3	419	4.66
NatEx	Chicago	late	111.4	431	5.43
NatEx	Chicago	late	114.8	509	5.73
NatEx	Chicago	late	116.6	584	6.63
NatEx	Chicago	late	116.7	282	4.56
NatEx	Chicago	late	116.9	607	7.05
NatEx	Chicago	late	118	392	5.03
NatEx	Chicago	late	119.2	475	6.12
NatEx	Chicago	late	119.3	365	6.01
NatEx	Chicago	ontime	119.4	530	6.8
NatEx	Chicago	ontime	119.9	499	6.52
NatEx	Chicago	ontime	120.4	380	5.96
NatEx	Chicago	ontime	122.2	476	5.59
NatEx	Chicago	ontime	125.6	469	5.67
NatEx	Chicago	ontime	126	343	5.69
NatEx	Chicago	ontime	126.7	298	6.43
NatEx	Chicago	late	127.2	716	7.14
NatEx	Chicago	late	128.4	421	5.82
NatEx	Chicago	ontime	128.5	436	6.1
NatEx	Chicago	ontime	129	562	6.53
NatEx	Chicago	ontime	129.8	468	6.58
NatEx	Chicago	ontime	130.2	552	6.3
NatEx	Chicago	ontime	131.9	553	6.67
NatEx	Chicago	ontime	134.4	396	6.66
NatEx	Chicago	ontime	139.1	463	6.62
NatEx	Chicago	ontime	139.5	585	6.52
NatEx	Chicago	ontime	151.7	398	6.31
NatEx	Chicago	ontime	156.2	676	8.34
NatEx	Denver	ontime	37.2	369	2.3
NatEx	Denver	ontime	72	420	3.55
NatEx	Denver	ontime	73.3	366	4.26
NatEx	Denver	ontime	74.1	332	3.23
NatEx	Denver	late	74.4	345	3.11
NatEx	Denver	ontime	76.5	546	4.43
NatEx	Denver	ontime	83.8	84	2.85
NatEx	Denver	ontime	65.6	285	3.61
NatEx	Denver	late	69.2	262	4.24
NatEx	Denver	ontime	70.3	121	3.08
NatEx	Denver	ontime	70.5	214	2.13
NatEx	Denver	ontime	72.2	403	4.49
NatEx	Denver	ontime	72.9	293	3.82
NatEx	Denver	ontime	73.7	148	2.95
NatEx	Denver	ontime	74.9	402	4.12
NatEx	Denver	ontime	75.2	378	4.13
NatEx	Denver	ontime	76	303	3.77
NatEx	Denver	ontime	76.7	357	4.15
NatEx	Denver	ontime	77.6	339	4.97
NatEx	Denver	ontime	78.1	321	3.89
NatEx	Denver	ontime	78.6	275	3.82
NatEx	Denver	ontime	79.7	162	3.7
NatEx	Denver	ontime	80.6	383	4.09
NatEx	Denver	late	80.7	546	5.47
NatEx	Denver	ontime	80.8	20	2.75
NatEx	Denver	ontime	82.7	508	5.3
NatEx	Denver	ontime	83	414	4.37
NatEx	Denver	ontime	83.3	264	3.86
NatEx	Denver	ontime	85.2	363	4.63
NatEx	Denver	late	87	345	4.49
NatEx	Denver	ontime	90	466	5.14
NatEx	Denver	ontime	90.1	286	4.34
NatEx	Denver	late	90.6	339	4.43
NatEx	Denver	ontime	90.8	286	4.08
NatEx	Denver	ontime	91	318	4.76
NatEx	Denver	ontime	91.3	542	5.72
NatEx	Denver	ontime	91.8	255	3.98
NatEx	Denver	late	91.9	337	4.19
NatEx	Denver	ontime	93.8	138	3.11
NatEx	Denver	ontime	95	474	5.33
NatEx	Denver	late	96	354	5.01
NatEx	Denver	late	96.3	487	4.67
NatEx	Denver	late	96.6	276	3.54
NatEx	Denver	late	97	442	5.29
NatEx	Denver	late	97.7	376	4.7
NatEx	Denver	late	99.2	417	5.43
NatEx	Denver	ontime	101.1	332	4.83
NatEx	Denver	ontime	101.4	446	5.38
NatEx	Denver	ontime	102.3	218	3.8
NatEx	Denver	late	104.7	424	4.84
NatEx	Denver	ontime	105.8	403	5.76
NatEx	Denver	ontime	108.4	383	5.24
NatEx	Denver	late	110.6	433	5.56
NatEx	Denver	ontime	110.8	554	5.45
NatEx	Denver	ontime	111.5	608	6.76
NatEx	Denver	late	117.6	696	7.91
NatEx	Denver	ontime	124.7	485	6.38
NatEx	Denver	ontime	125.6	498	6.2
NatEx	Denver	ontime	134.1	734	7.73
NatEx	Denver	ontime	155.1	638	8.18