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:



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. There is no difference between male and female skiers in the proportions who never, occasionally, and always use a ski helmet.
B. There is no correlation between ski helmet usage and gender.
C. The proportions of males and females skiers are equal.
D. Male and female skiers are as likely to never use a ski helmet as always use one.
E. 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.


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.


Part c)
Perform a suitable test in R on the data above to test the null hypothesis.

Provide the value of your test statistic to 2 decimal places.


Part d)
Under the null hypothesis, the test statistic should be an observation from which probability distribution?

A. The Chi-squared distribution on two degrees of freedom.
B. The Chi-squared distribution on four degrees of freedom.
C. The $F_{3,707}$ distribution.
D. The standard Normal distribution.
E. The $t$ distribution on two degrees of freedom.
F. The Chi-squared distribution on five degrees of freedom.


Part e)
Would you reject or not reject your null hypothesis at the 5 % significance level?

A. Not reject
B. Reject