Question

Put a box around the relevant portion of the printout. The results below show the analysis of the number of professional ballplayers born in each month of the year for one season of professional baseball.  Conduct the appropriate hypothesis test to determine if baseball players’ birth months are uniformly distributed.

1. Hypotheses IN THE CONTEXT OF THE QUESTION

2. Test Statistic Type and value and p-value

3. Conclusion in a complete sentence IN THE CONTEXT OF THE QUESTION

4. Explanation of the differences in a complete sentence in the context of the problem.

Category	Observed	Expected	Contribution to Chi-Square
January	137	123.167	1.5537
February	121	123.167	0.0381
March	116	123.167	0.4170
April	121	123.167	0.0381
May	126	123.167	0.0652
June	114	123.167	0.6822
July	102	123.167	3.6376
August	165	123.167	14.2086
September	134	123.167	0.9529
October	115	123.167	0.5415
November	105	123.167	2.6795
December	122	123.167	0.0111

Put a box around the relevant portion of the printout.

Answer 1

a)

Ho: The baseball players birth month are uniformly distributed

Vs

H1:The birth months are not uniformly distributed

b)

Test statistic

This is just the sum of contribution to Chi-square values.

P-value is

is the chi square distribution with (n-1)=11 df.

c) As the p-value is less than 0.05, we reject the Null hypothesis at 5% LOS that is we can conclude that the birth months of baseball players are not uniformly distributed.

d)

The contirbution to Chi square is calculated as

where O is observed value and E is expected value.

Thank you !!