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NFL player survey. Researchers at the University of
Chapter 6, Problem 87E(choose chapter or problem)
Problem 87E
NFL player survey. Researchers at the University of Pennsylvania’s Wharton Sports Business Initiative collaborated with the National Football League Players Association (NFLPA) to produce the first NFL Player Survey. Of the 1,696 active NFL players, 1,355 (almost 80%) responded to the survey. One of the survey questions asked, “Who is the coach—professional, college, or high school—that has been the most influential in your career?” Of the 1,355 respondents, 759 selected an NFL (professional) coach.
a. Construct a 95% confidence interval for the true proportion of active NFL players who select a professional coach as the most influential in their careers.
b. Why is it necessary to use the continuity correction factor in the construction of the interval, part a?
c. Give a practical interpretation of the interval, part a.
Questions & Answers
QUESTION:
Problem 87E
NFL player survey. Researchers at the University of Pennsylvania’s Wharton Sports Business Initiative collaborated with the National Football League Players Association (NFLPA) to produce the first NFL Player Survey. Of the 1,696 active NFL players, 1,355 (almost 80%) responded to the survey. One of the survey questions asked, “Who is the coach—professional, college, or high school—that has been the most influential in your career?” Of the 1,355 respondents, 759 selected an NFL (professional) coach.
a. Construct a 95% confidence interval for the true proportion of active NFL players who select a professional coach as the most influential in their careers.
b. Why is it necessary to use the continuity correction factor in the construction of the interval, part a?
c. Give a practical interpretation of the interval, part a.
ANSWER:
Answer
Step 1 of 3
(a)
Of the 1,696 active NFL players, 1,355 (almost 80%) responded to the survey. One of the survey questions asked, “Who is the coachprofessional, college or high school
that has been the most influential in you career?”
Of the 1,355 respondents, 759 selected an NFL (professional), coach.
We are asked to construct a 95% CI for the true proportion of active NFL players who select a professional coach as the most influential in their career.
The formula for computing the sample proportion is
We have given
Then a level confidence interval for p (proportion) is
………..(1)
For a 95% confidence interval, the value of is,
and
Then for
is
, hence
Finite population correction factor: The term that is used in the formulas for
and
whenever a finite population, rather than an infinite population, is being sampled.
The generally accepted rule of thumb is to ignore the finite population correction factor whenever
Since,
We need to use the population correction factor because of
Hence the 95% confidence interval for p (proportion) after finite population correction from equation (1),
Hence a 95% CI for the true proportion of active NFL players who select a professional coach as the most influential in their career is