Birth month is related to success in many youth sports. This is known as the relative age effect (RAE). The RAE in youth sports is exhibited by the presence of fewer members of an age group born in the months further from the age-cutoff date for the sport (January 1 for most youth soccer leagues). These older players, due to their physical and psychological advantages, are more likely to be identified as talented and therefore are selected for advancement in the youth soccer academies.

While these differences are crucial in the selection process during adolescence, is there evidence that RAE carries over to adult players? In this problem we examine whether RAE exists in the top level European soccer leagues: Ligue 1 and Ligue 2 in France, Bundesliga 1 and Bundesliga 2 in Germany, Seire A and Serie B in Italy, Premier League and Championship in England, and 1st Division and 2nd Division in Spain.

The table below shows in the first column the birthdays by month of 5507 male players who played during a recent season in the leagues mentioned above. Also shown in the second column, based on national demographic statistics, is the percentage of the general population born in each month. Does the distribution of birth months of elite European soccer players differ from the distribution of birth months of the general population? Perform the appropriate hypothesis test.

Month	Observed Birthdays	General Population %	Expected Birthdays
January	593	8%	440.56
February	549	7%	385.49
March	581	8%	440.56
April	497	8%	440.56
May	503	8%	440.56
June	450	8%	440.56
July	403	9%	495.63
August	434	9%	495.63
September	414	9%	495.63
October	365	9%	495.63
November	364	8%	440.56
December	354	9%	495.63
Total	5507	100	5507

Question 1. In the calculation of the test statistic for this hypothesis test, what numerical value does the month of October contribute to the test statistic?

(round to 2 decimal places)

Question 2. What is the value of the test statistic for this hypothesis test?

(round to 2 decimal places)

Question 3. Choose the correct expression for the P-value for this hypothesis test.

• 0.10 < P-value < 0.20
• P-value < 0.0001
• 0.01 < P-value < 0.05
• 0.001 < P-value < 0.002
• 0.05 < P-value < 0.10
• P-value > 0.20

Question 4. What is the correct conclusion for this hypothesis test? (one submission only)

• Reject the null hypothesis and conclude that there is evidence that the distribution of birth months for elite European soccer players differs from the distribution of birth months for the general population since more soccer players than expected are born in the first half of the year.
• Do not reject the null hypothesis and conclude that there is no evidence that the distribution of birth months for elite European soccer players differs from the distribution of birth months for the general population.
• Reject the null hypothesis and conclude that there is evidence that the distribution of birth months for elite European soccer players differs from the distribution of birth months for the general population since more soccer players than expected are born in the second half of the year.