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 Always 241 84 169 106 31 79 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. Part a) 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.

Answer 1

Answer:

To test,

Ho:There is no relationship between Gender and Helmate usage

H1:There is relationship between Gender and Helmate usage

ans a)

c) There is no relationship between Gender and Helmate usage

			Melmate Usage
		Never	occasionally	Alwas	Total
Gender	male	241	84	169	494
	female	106	31	79	216
	Toatal	347	115	248	710

=$Expected frequency=\frac{\sum row*\sum column}{\sum Total}$

			Melmate Usage
		Never	occasionally	Alwas	Total
Gender	male	241.4338	80.01408	172.5521	494
	female	105.5662	34.98592	75.44789	216
	Total	347	115	248	710

ans b)

From above expected ffrequency table,

The expected number of men in the survey who never wear a ski helmet is 241.43

ans c)

$\chi ^2=\sum (Oi-Ei)^2/Ei$

			Melmate Usage
		Never	occasionally	Alwas	Total
Gender	male	0.000779	0.198559	0.073123	0.272461
	female	0.001783	0.454112	0.167235	0.623129
	Total	0.002562	0.652671	0.240358	0.895591

Test statistic= 0.89

ans d)

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

e)

P value= 0.6390

Where, P value > 0.05

We accept Ho