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.)
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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.
orchestra answered 2 years agoRelated Solutions
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Round
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75
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