Question

ST231 S20 HW6: Problem 4 Previous Probler Problem List Next Problem (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 Always 231 80 183 106 33 77 Gender Male Female Ruzic, L. and Tudor, A. (2011): Risk-taking behaviour in skiing among helmet wearers and nonwearers. Wilderness and Environmental Medicine, 291-296. Parta) Which of the following null hypotheses could sensibly be tested by the data presented above? A. The proportions of males and females skiers are equal. B. 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. C. There is no relationship between Gender and Helmet usage. D. Male and female skiers are as likely to never use a ski helmet as always 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 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 distribution on two degrees of freedom. B. The standard Normal distribution. C. The F3,707 distribution. D. The Chi-squared distribution on four degrees of freedom. E. The Chi-squared distribution on two degrees of freedom. F. The Chi-squared distribution on five degrees of freedom. Parte) Would you reject or not reject your null hypothesis at the 5 % significance level? A. Reject B. Not reject Note: You can earn partial credit on this problem.

Answer 1

a)

C. There is no relationship between Gender and Helmet usage.

b)

Expected	Ei=row total*column total/grand total	Never	Occasionally	Always	Total
	Male	234.4761	78.6225	180.9014	494
	Female	102.5239	34.3775	79.0986	216
	total	337	113	260	710
chi square    χ2	=(Oi-Ei)2/Ei	Never	Occasionally	Always	Total
	Male	0.052	0.024	0.024	0.1000
	Female	0.118	0.055	0.056	0.2287
	total	0.1694	0.0793	0.0800	0.3287
test statistic X2=		0.3287

expected number of male who never went to ski =234.48

c)

value of test statistic =0.33

d)

E. The Chi-squared distribution on two degrees of freedom.

e)

B) not reject