Question

(1 point) Do male and female skiers differ in their tendency to use a ski helmet? Ruzic and Tudor (2011) report a study in which 710 skiers completed a survey about aspects of their skiing habits. Suppose the results from the question on the survey about ski helmet usage were as follows: Helmet Usage Never Occasionally 242 Gender Always 180 72 Male Female 82 Ruzic, L. and Tudor, A. (2011): Risk-taking behaviour in skiing among helmet wearers and nonwearers. Wilderness and Environmental Medicine, 291-296. Part a) Which of the following hypotheses could sensibly be tested by the data presented above? A. The mean number of male skiers who never wear a ski helmet is the same as the mean number of female skiers who never use one. B. Male and female skiers are as likely to never use a ski helmet as always use one. C. There is no difference between male and female skiers in the proportions who never, occasionally, and always use a ski helmet. D. The proportions of males and females skiers are equal. E. There is no correlation between ski helmet usage and gender. Part b) Under the null hypothesis, what is the expected number of men in the survey who never wear a ski helmet? Give your answer to 2 decimal places.

Answer 1

Helmet Usage

Gender	Never	occasionally	Always	total
male	242	72	180	494
female	94	40	82	216
total	336	112	262	710

a) The hypothesis could sensibly tested by the following data,

C) There is no difference between male and female skiers in the proportions who never , occasionally and always use a ski helmet.

b) The expected number of men in the survey who never wear a ski helmet under null hypothesis,

E = (336*494) / 710 = 165984 / 710 = 233.78

c) The test statistic is given by,

  

? = ΠΣΣ - 1)

x | 949279x 180 9: 40? = 7101- 336 + 494*112 + 494262 * 494336 + 216 | 112 + 216 十 s2 262 + 216 -1)

  

x = 710(1.00355838-1)

= 2.53 (ans)

with degrees of freedom , (3-1)*(2-1)= 2

d) Under null hypothesis, the test statistic should be from,

F) The chi-squared distribution on two degrees of freedom.

e)At 5% significance level, $\chi^{2}_{0.05,2}$ = 5.991 > $\chi^{2}$ = 2.53

we do not reject the null hypothesis.

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