Question

Data lists number of baseball players with birth dates in the first four months of the year.

Month	January	February	March	April
Number of players	387	329	367	345

Find the P-value to test the claim that baseball players are born in the first four months of the year with the same frequency.

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Answer 1

Given :

Data lists number of baseball players with birth dates in the first four months of the year.

Month	January	February	March	April
Number of players	387	329	367	345

Hypothesis test :

The null and alternative hypothesis is

Ho : p1 = p2 = p3 = p4 = 1/4 = 0.25

Ha : At least one proportion not equal.

Chi square goodness of fit test :

Expected frequency = n*p

Month	Observed frequency(O)	Expected frequency(E)	(O-E)^2/E
January	387	1428*0.25 = 357	2.521
February	329	357	2.1961
March	367	357	0.2801
April	345	357	0.4034
Total	1428	1428	5.4006

Test statistic :

= (O-E)^2/E = 5.401

Degree of freedom = df = k-1 = 4-1 = 3

P-value :

P-value corresponding to = 5.401 with df = 3 is 0.1447.

So P-value is 0.1447