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Course Documents

Chapter 1 - Intro

Chapter 2 - Methods for Describing Sets of Data

Chapter 3 - Probability

Chapter 4 - Discrete Random Variables

Chapter 5 - Normal Random Variables

Chapter 6 - Sampling Distributions

Chapter 7 - Confidence Intervals

Chapter 8 - Tests of Hypothesis: One Sample

Chapter 9 - Confidence Intervals and Hypothesis Tests: Two Samples

Sample Exam I: Chapters 1 & 2

Sample Exam II: Chapters 3 & 4

Sample Exam III: Chapters 5 & 6

Sample Exam IV: Chapters 7 & 8

Example 113.5

Example 113.5: In many sports, eligibility for minor leagues is determined by age at the start of the calendar year (Jan 1).  Journalist Malcolm Gladwell wrote about the effects of this eligibility rule on Canadian hockey in his 2008 book Outliers.  The issue is that people born in the early months of the year end up being older when they are finally able to participate in minor leagues than students born in later months.  For example, a child born on January 2nd who is eligible to play when he/she turns ten, will be 10 years and 364 days old when he starts playing compared to a child born December 31st who will only be 10 years and 1 day old when he/she is eligible to play.   Being older is an advantage in sports, so these older kids naturally perform better and stand out more to coaches and scouts. 

Stephen Leavitt and Stephen J. Dubner, authors of the bestselling Freakonomics series of books, noted this trend in international soccer in a 2006 New York Times column.  FIFA introduced a Jan. 1 cutoff date in 1997. Of the 410 players in the 2006 World Cup born after 1979 (thus affected by the Jan. 1 cutoff date) the percentage who were born in January, February and March was 32.4%.  Use the 2006 World Cup Data and a 99% confidence level to form an interval estimate for the true proportion of FIFA players born after 1979 that have a birthday in the first three months of the year.  Assuming that for the general population the birth rate for the months January, February, and March is approximately 25%, does it seem the proportion of FIFA stars born in these three months is significantly higher than the expected 25% rate?

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