Chi-Square Good of Fit Problem:Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that the younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtained information about registered drivers from the Department of Motor Vehicles (DMV) and selected a sample of n = 300 accidents reports from the police department. The DMV reports the percentage of registered drivers in each age category as follows: 16% are younger than age 20,; 28%are 20 to 29 years old;and 56% are age 30 and older. The number of accidents reports for each age group is as follows:Under age 20 Age 20-29 Age 30 and older68 92 140Is there a difference between the three age groups? Test with alpha = .05 Remember use the table on 582 for critical region values. 582APPENDIX B STATISTICAL TABLESTABLE B.7THE CHI-SQUARE DISTRIBUTION**The table entries are critical values of x².CriticalProportion in Critical Regiondf0.100.050.0250.010.00512.713.845.026.637.8824.615.997.389.2110.6036.257.81-9.3511.3412.8447.789.49.11.1413.2814.8659.2411.0712.8315.0916.75610.6412.5914.45´ 16.8118.55712.0214.0716.0118.4820.288.13.3615.5117.5320.0921.9616.9219.0221.6723.5914.6815.999.1018.3120.4823.2125.191117.2819.6821.9224.7226.761218.5521.0323.3426.2228.3022.3624.7427.6929.8219.8121.061329.1431.3223.6825.001426.121522.3127.4930.5832.801623.5426.3028.8532.0034.271724.7727.5930.1933.4135.721825.9928.8731.5334.8137.161927.2030.1432.8536.1938.582028.4131.4134.1737.5740.0038.9341.4035.4836.782129.6232.672230.8133.9240.2942.802332.0135.1738.0841.6444.182433.2036.4239.3642.9845.562534.3837.6540.6544.3146.932635.5638.8941.9245.6448.292736.7440.1143.1946.9649.642837.9241.3444.4648.2850.992939.0942.5645.7249.5952.343040.2643.7746.9850.8953.674051.8155.7659.3463.6966.775063.1767.5071.4276.1579.496074.4079.0883.3088.3891.957085.5390.5395.02100.42104.22116.32112.33124.128096.58101.88106.63113.14118.14128.30107.56118.5090100124.34129.56135.81140.17Table 8 of Pearson, E., and Hartley, H. O. (1966). Biometrika Tables for Statisticians(3rd ed.). New York: Cambridge University Press. Adapted and reprinted with permissionof the Biometrika trustees.

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Answered: Image /qna-images/answer/adf6e731-fae4-4d9e-bae5-588ea62e96f0.jpgDegree of freedom = k-1 = 3-1 = 2 critical value - 5.99

Answered: Chi-Square Good of Fit Problem:…

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Chi-Square Good of Fit Problem:

Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that the younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtained information about registered drivers from the Department of Motor Vehicles (DMV) and selected a sample of n = 300 accidents reports from the police department. The DMV reports the percentage of registered drivers in each age category as follows: 16% are younger than age 20,; 28%are 20 to 29 years old;and 56% are age 30 and older. The number of accidents reports for each age group is as follows:

Under age 20 Age 20-29 Age 30 and older

68 92 140

Is there a difference between the three age groups? Test with alpha = .05 Remember use the table on 582 for critical region values.

582
APPENDIX B STATISTICAL TABLES
TABLE B.7
THE CHI-SQUARE DISTRIBUTION*
*The table entries are critical values of x².
Critical
Proportion in Critical Region
df
0.10
0.05
0.025
0.01
0.005
1
2.71
3.84
5.02
6.63
7.88
2
4.61
5.99
7.38
9.21
10.60
3
6.25
7.81-
9.35
11.34
12.84
4
7.78
9.49.
11.14
13.28
14.86
5
9.24
11.07
12.83
15.09
16.75
6
10.64
12.59
14.45
´ 16.81
18.55
7
12.02
14.07
16.01
18.48
20.28
8.
13.36
15.51
17.53
20.09
21.96
16.92
19.02
21.67
23.59
14.68
15.99
9.
10
18.31
20.48
23.21
25.19
11
17.28
19.68
21.92
24.72
26.76
12
18.55
21.03
23.34
26.22
28.30
22.36
24.74
27.69
29.82
19.81
21.06
13
29.14
31.32
23.68
25.00
14
26.12
15
22.31
27.49
30.58
32.80
16
23.54
26.30
28.85
32.00
34.27
17
24.77
27.59
30.19
33.41
35.72
18
25.99
28.87
31.53
34.81
37.16
19
27.20
30.14
32.85
36.19
38.58
20
28.41
31.41
34.17
37.57
40.00
38.93
41.40
35.48
36.78
21
29.62
32.67
22
30.81
33.92
40.29
42.80
23
32.01
35.17
38.08
41.64
44.18
24
33.20
36.42
39.36
42.98
45.56
25
34.38
37.65
40.65
44.31
46.93
26
35.56
38.89
41.92
45.64
48.29
27
36.74
40.11
43.19
46.96
49.64
28
37.92
41.34
44.46
48.28
50.99
29
39.09
42.56
45.72
49.59
52.34
30
40.26
43.77
46.98
50.89
53.67
40
51.81
55.76
59.34
63.69
66.77
50
63.17
67.50
71.42
76.15
79.49
60
74.40
79.08
83.30
88.38
91.95
70
85.53
90.53
95.02
100.42
104.22
116.32
112.33
124.12
80
96.58
101.88
106.63
113.14
118.14
128.30
107.56
118.50
90
100
124.34
129.56
135.81
140.17
Table 8 of Pearson, E., and Hartley, H. O. (1966). Biometrika Tables for Statisticians
(3rd ed.). New York: Cambridge University Press. Adapted and reprinted with permission
of the Biometrika trustees.

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