Problem 16BSC
In Exercise, test the given claim.
Injuries and Motorcycle Helmet Color A casecontrol (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 table below (based on data from “Motorcycle Rider Conspicuity and Crash Related Injury: CaseControl Study,” by Wells et al., BMJ USA, Vol. 4). Test the claim that injuries are independent of helmet color. Should motorcycle drivers choose helmets with a particular color? If so, which color appears best?

Color of Helmet 


Black 
White 
Yellow/Orange 
Red 
Blue 
Controls (not injured) 
491 
377 
31 
170 
55 
Cases (injured or killed) 
213 
112 
8 
70 
26 
Answer:
Step 1 of 2</p>
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
H0: The claim that the amount of smoking is independent of seat belt use
H1: The claim that the amount of smoking is not independent of seat belt use
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chisquare test for independence.
Applying the chisquare test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chisquare test statistic.
DF = (r  1) (c  1) = (2  1) (5  1) = 4
 Color of Helmet  
 Black  White  Yellow/Orange  Red  Blue  Total 
Controls (not injured)  491  377  31  170  55  1124 
Cases (injured or killed)  213  112  8  70  26  429 
Total  704  489  39  240  81  1553 