Most alpine skiers and snowboarders do not use helmets. Do helmets reduce the ri

Question

Most alpine skiers and snowboarders do not use helmets. Do helmets reduce the risk of head injuries? A study in Norway compared skiers and snowboarders who suffered head injuries with a control group who were not injured. Of 578 injured subjects, 96 had worn a helmet. Of the 2992 in the control group, 649 wore helmets. Is helmet use less common among skiers and snowboarders who have head injuries? Follow the four-step process as illustrated in Examples 23.4 and 23.5. (Note that this is an observational study that compares injured and uninjured subjects. An experiment that assigned subjects to helmet and no-helmet groups would be more convincing.) Solve (continue): Give the value of the test statistic z. (Round your answer to two decimal places.) z = Solve (continue): What is the P-value for the test? (Round your answer to four decimal places.) P-value =

Explanation / Answer

Hypothesis:

H0: p1 = p2

Ha : p1 < p2

Test statistic:

p1 = 96/578 = 0.166 , n1 = 578 , p2 = 649 / 2992 = 0.217 , n2 = 2992

  p = (p1 * n1 + p2 * n2) / (n1 + n2)

= [(0.166 * 578) + (0.217 * 2992)] / (578 + 2992)

= 0.209

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = sqrt [ 0.209 * 0.791 * ( 1/578 + 1/2992 ) ]

= 0.018

z = (p1 - p2) / SE

= (0.166 - 0.217)/0.018

= -2.83

Now, we need to find p value using z =-2.83

P value = 0.002327.

As p value is less than significance level 0.05. So, we reject the null hypothesis

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