A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a0.05 significance level, test the claim that injuries are independent of helmet color. Color of Helmet
A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a0.05 significance level, test the claim that injuries are independent of helmet color. Color of Helmet
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Transcribed Image Text:A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.05 significance level, test the claim that injuries are independent of helmet color.
Color of Helmet
Black
White
Yellow
Red
Blue
Controls (not injured)
Cases (injured or
killed)
479
349
36
161
87
211
111
67
43
Click here to view the chi-square distribution table.
Chi-square distribution table
Identify the null and alternative hypotheses. Choose the correct answer below.
O A. Ho: Whether a crash occurs and helmet color are independent
H: Whether a crash occurs and helmet color are dependent
O B. Ho: Injuries and helmet color are dependent
Area to the Right of the Critical Value
Degrees of
Freedom
H1: Injuries and helmet color are independent
0.995
0.99
0.975
0.95
0.90
0.10
O C. Ho: Whether a crash occurs and helmet color are dependent
1
0.001
0.004
0.016
2.706
2
0.010
0.020
0.051
0.103
0.211
4.605
H,: Whether a crash occurs and helmet color are independent
0.072
0.207
3
0.115
0.216
0.352
0.584
6.251
O D. Ho: Injuries and helmet color are independent
4
0.297
0.484
0.711
1.064
7.779
0.412
0.554
0.831
1.145
1.610
9.236
H,: Injuries and helmet color are dependent
6
0.676
0.872
1.237
1.635
2.204
10.645
Compute the test statistic.
7
0.989
1.239
1.690
2.167
2.833
12.017
8
1.344
1.646
2.180
2.733
3.490
13.362
9
1.735
2.088
2.700
3.325
4.168
14.684
(Round to three decimal places as needed.)
10
2.156
2.558
3.247
3.940
4.865
15.987
Find the critical value(s).
Print
Done
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
What is the conclusion based on the hypothesis test?
Ho. There
sufficient evidence to warrant rejection of the claim that injuries are independent of helmet color.
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