Discussion about a chi-square statistics

Question

Assignment:

Q1. In 1978, a small plane slammed into a passenger jet over San Diego, killing 144 people. Langhorne Bond, then the head of the FAA, responded by proposing strict new curbs on small planes around many busy airports.

Examine the following FAA data. Is there a statistically significant difference in the frequency of different types of near midair collisions between the first 6 months of 1985 and the first 6 months of 1986? A corporate plane in this case, means a UPS or FEDEX type of aircraft.

Type of Incident Jan-July '85 Jan-July '86
O E O E
2 airliners 15 16.6 19 17.4

1 airliner and
1 corporate plane 99 112 130 117

2 corporate planes 262 247.4 244 258.6

TOTAL 376 393

Table of Chi-square statistics
F-statistics with other P-values: P=0.05 | P=0.01 | P=0.001
df	P = 0.05	P = 0.01	P = 0.001
1	3.84	6.64	10.83
2	5.99	9.21	13.82
3	7.82	11.35	16.27
4	9.49	13.28	18.47
5	11.07	15.09	20.52
6	12.59	16.81	22.46
7	14.07	18.48	24.32
8	15.51	20.09	26.13
9	16.92	21.67	27.88
10	18.31	23.21	29.59
11	19.68	24.73	31.26
12	21.03	26.22	32.91
13	22.36	27.69	34.53
14	23.69	29.14	36.12
15	25	30.58	37.7
16	26.3	32	39.25
17	27.59	33.41	40.79
18	28.87	34.81	42.31
19	30.14	36.19	43.82
20	31.41	37.57	45.32
21	32.67	38.93	46.8
22	33.92	40.29	48.27
23	35.17	41.64	49.73
24	36.42	42.98	51.18
25	37.65	44.31	52.62
26	38.89	45.64	54.05
27	40.11	46.96	55.48
28	41.34	48.28	56.89
29	42.56	49.59	58.3
30	43.77	50.89	59.7
31	44.99	52.19	61.1
32	46.19	53.49	62.49
33	47.4	54.78	63.87
34	48.6	56.06	65.25
35	49.8	57.34	66.62
36	51	58.62	67.99
37	52.19	59.89	69.35
38	53.38	61.16	70.71
39	54.57	62.43	72.06
40	55.76	63.69	73.41
41	56.94	64.95	74.75
42	58.12	66.21	76.09
43	59.3	67.46	77.42
44	60.48	68.71	78.75
45	61.66	69.96	80.08
46	62.83	71.2	81.4
47	64	72.44	82.72
48	65.17	73.68	84.03
49	66.34	74.92	85.35
50	67.51	76.15	86.66
51	68.67	77.39	87.97
52	69.83	78.62	89.27
53	70.99	79.84	90.57
54	72.15	81.07	91.88
55	73.31	82.29	93.17
56	74.47	83.52	94.47
57	75.62	84.73	95.75
58	76.78	85.95	97.03
59	77.93	87.17	98.34
60	79.08	88.38	99.62
61	80.23	89.59	100.88
62	81.38	90.8	102.15
63	82.53	92.01	103.46
64	83.68	93.22	104.72
65	84.82	94.42	105.97
66	85.97	95.63	107.26
67	87.11	96.83	108.54
68	88.25	98.03	109.79
69	89.39	99.23	111.06
70	90.53	100.42	112.31
71	91.67	101.62	113.56
72	92.81	102.82	114.84
73	93.95	104.01	116.08
74	95.08	105.2	117.35
75	96.22	106.39	118.6
76	97.35	107.58	119.85
77	98.49	108.77	121.11
78	99.62	109.96	122.36
79	100.75	111.15	123.6
80	101.88	112.33	124.84
81	103.01	113.51	126.09
82	104.14	114.7	127.33
83	105.27	115.88	128.57
84	106.4	117.06	129.8
85	107.52	118.24	131.04
86	108.65	119.41	132.28
87	109.77	120.59	133.51
88	110.9	121.77	134.74
89	112.02	122.94	135.96
90	113.15	124.12	137.19
91	114.27	125.29	138.45
92	115.39	126.46	139.66
93	116.51	127.63	140.9
94	117.63	128.8	142.12
95	118.75	129.97	143.32
96	119.87	131.14	144.55
97	120.99	132.31	145.78
98	122.11	133.47	146.99
99	123.23	134.64	148.21
100	124.34	135.81	149.48

Q2. The following data represents a study of a main street in your town USA. The city monitored speeds on main-street before a stop light was installed. They then conducted a study after a stop light was installed to see if there was an effect on the speed of the cars cruising down main-street. At 95% level of confidence.

Direction Before the Stop Light After Stop Light

9 am Westbound 32.1 32.2
9 am eastbound 32.2 32.9

1 pm westbound 32.6 32.4
1 pm eastbound 33 31

8 pm westbound 31.2 31.4
8 pm eastbound 33.5 31.6

Use T-test for paired data

Q3. Calculate the following at a .05 level of significance:

Population 1 Population 2
Sample size n1 = 30 n2 = 35
Sample mean xbar1 = 22.3 xbar2 = 18.5
Sample st. dev s1 = 1.5 s2 = 2.2

Use Z-test for unpaired data