Question

In: Statistics and Probability

the amateur triathletes who competed in the 2006 ironman Coeur d'Alene were classified by sex and...

the amateur triathletes who competed in the 2006 ironman Coeur d'Alene were classified by sex and age with the following results (ford ironman coeur d'alene 2006 results, 2006.)

18-34 35-49 50+
men 467 950 208
women 229 304 42

Do these data provide sufficient evidence at the 0.05 significance level to conclude that sex and age are related among triathletes who complete in Coeur d'Alene?

Solutions

Expert Solution

Observed Frequencies
18-34 35-49 50+ Total
Men 467 950 208 1625
Women 229 304 42 575
Total 696 1254 250 2200
Expected Frequencies
18-34 35-49 50+ Total
Men 696 * 1625 / 2200 = 514.0909 1254 * 1625 / 2200 = 926.25 250 * 1625 / 2200 = 184.6591 1625
Women 696 * 575 / 2200 = 181.9091 1254 * 575 / 2200 = 327.75 250 * 575 / 2200 = 65.3409 575
Total 696 1254 250 2200
(fo-fe)²/fe
Men (467-514.0909)²/514.0909= 4.3135 (950-926.25)²/926.25=0.609 (208-184.6591)²/184.6591=2.9503
Women (229-181.9091)²/181.9091=12.1905 (304-327.75)²/327.75= 1.721 (42-65.3409)²/65.3409 = 8.3378

Null and Alternative hypothesis:  

Ho: Factors are independent.  

H1: Factor are dependent.  

Test statistic:  

χ² = ∑ ((fo-fe)²/fe) =    30.1221

df = (r-1)(c-1) =    2

p-value = CHISQ.DIST.RT(30.1221, 2) = 0.000

Decision:  

p-value < α, Reject the null hypothesis.  

There is enough evidence to conclude that sex and age are related.


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