Hockey - Birthdays: It has been observed that a large percentage of professional
ID: 2926205 • Letter: H
Question
Hockey - Birthdays: It has been observed that a large percentage of professional hockey players have birthdays in the first part of the year. It has been suggested that this is due to the cut-off dates for participation in the youth leagues - those born in the earlier months are older than their peers and this advantage is amplified over the years via more opportunities to train and be coached. Of the 511 professional hockey players in a season, 157 of them were born in January, February, or March.
(a) Assume that 25% of birthdays from the general population occur in January, February, or March (these actually contain 24.7% of the days of the year). In random samples of 511 people, what is the mean number of those with a birthday in January, February, or March? Round your answer to one decimal place. = ____
(b) What is the standard deviation? Round your answer to one decimal place. = _____
(c) Now, 157 of the 511 professional hockey players were born in the first three months of the year. With respect to the mean and standard deviation found in parts (a) and (b) what is the z-score for 157? Round your answer to two decimal places. z =____
(d) If the men in the professional hockey league were randomly selected from the general population, would 157 players out of 511 be an unusual number of men born in the first 3 months of the year?
____Yes, that is an unusual number.
______No, that is not unusual.
(e) Which of the following is an acceptable sentence to explain this situation?
_____If the men in the professional hockey league were selected randomly from the general population, this would be an unusual collection of birth dates.
_____There is good reason to believe that a significantly larger than expected proportion of professional hockey league players are born in the first three months of the year.
_____This could be a result of the random variation of birth dates within a sample. However, it would be pretty unlikely to happen by chance.
_____All of these are valid statements.
Explanation / Answer
(a) Assume that 25% of birthdays from the general population occur in January, February, or March (these actually contain 24.7% of the days of the year). In random samples of 511 people, what is the mean number of those with a birthday in January, February, or March? Round your answer to one decimal place.
= 511 * 25/100 = 127.8
(b) What is the standard deviation? = sqrt (511 * 0.25 * 0.75) = 9.8
(C) Now, 157 of the 511 professional hockey players were born in the first three months of the year. With respect to the mean and standard deviation found in parts (a) and (b) what is the z-score for 157?
Z = (157 - 127.8)/ 9.8 = 2.98
(D) If the men in the professional hockey league were randomly selected from the general population, would 157 players out of 511 be an unusual number of men born in the first 3 monthsof the year?
Pr(Z > 2.98) = 0.0014
so yes, it is a unusual number.
(E) Which of the following is an acceptable sentence to explain this situation?
(II) There is good reason to believe that a significantly larger than expected proportion of professional hockey league players are born in the first three months of the year.
OPtion 2 is true here
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