Barnsley, Thompson, and Barnsley (1985, p. 24) examined the birth months of National Hockey League players in the United States and Canada. They hypothesized that traditional rules stating that a player must be born before January 1 to join the youth hockey team for a particular age group would mean that older players would be put on better teams because they were bigger and more physically developed. This would give them an advantage in their youth sports training over younger players. According to their data, professional hockey players were born in the following months. The null hypothesis for their study was that players were equally likely to be born each month, which would produce an equal number of players born each month (with a proportion of 1/12 or .083 born each month).

a. How many degrees of freedom are in Barnsley et al.’s (1985) data?
b. If α = .05, what is the χ²_crit value for the data?

c. Calculate the χ²_obs value.

d. Compare the χ²_crit value and the χ²_obs value. Should you reject or retain the null hypothesis in this example?

e. Calculate an odds ratio for each month.

f. Interpret these odds ratios.

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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total 81 69 79 72 78 63 46 45 66 38 45 33 715