Question

In: Statistics and Probability

Birth Date and Canadian Ice Hockey In his book Outliers: The Story of Success (2008), Malcolm...

Birth Date and Canadian Ice Hockey

In his book Outliers: The Story of Success (2008), Malcolm Gladwell speculates that Canadian ice hockey players that are born early in the year have an advantage. This is because the birthdate cutoff for different levels of youth hockey leagues in Canada is January 1st, so youth hockey players who are born in January and February are slightly older than teammates born later in the year. Does this slight age advantage in the beginning lead to success later on? A 2010 study1 examined the birthdate distribution of players in the Ontario Hockey League (OHL), a high-level and selective Canadian hockey league (ages 15-20), for the 2008–2009 season. The number of OHL players born during the 1st quarter (Jan–Mar), 2nd quarter (Apr–Jun), 3rd quarter (Jul–Sep), and 4th quarter (Oct–Dec) of the year is shown in the table below. The overall percentage of live births in Canada (year 1989) are also provided for each quarter. Is this evidence that the birthdate distribution for OHL players differs significantly from the national proportions? Calculate the chi-square statistic, find the p-value, and state the conclusion in context.

Qtr 1 Qtr 2 Qtr 3 Qtr 4
OHL Player 147 110 52 50
% of Canadian births 23.7% 25.9% 25.9% 24.5%


Table 1 Birthdates nationally in Canada and for elite hockey players
1Nolan, J. and Howell, G., "Hockey success and birth date: The relative age effect revisited," International Review of Sociology of Sport, 2010; 45(4): 507–512.

Calculate the chi-square test statistic and the p-value.

Round your answer for the chi-square statistic to two decimal places, and your answer for the p-value to three decimal places.

χ2= __________________________

p-value = ______________________

Is there evidence that the birthdate distribution for OHL players differs significantly from the national proportions?

Yes or No?

Solutions

Expert Solution

Categories Observed Expected (fo-fe)2/fe
Qrt1 147 359*0.237=85.083 (147-85.083)2/85.083 = 45.059
Qtr2 110 359*0.259=92.981 (110-92.981)2/92.981 = 3.115
Qtr3 52 359*0.259=92.981 (52-92.981)2/92.981 = 18.062
Qtr4 50 359*0.245=87.955 (50-87.955)2/87.955 = 16.379
Sum = 359 359 82.614

The P-Value is < .00001. The result is significant at p < .05.


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