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You may recall that in recent National Football League history, Tom Brady and the New England Patriots were accused of deliberately deflating footballs in order to give themselves a competitive advantage on the football playing field. Presumably, one advantage of playing with a deflated football is that the ball is easier to grip..not only for the quarterback but for everyone who touches it. If the ball is easier to grip, players would fumble it less often. So, one way to examine if the Patriots actually had a competitive advantage due to deflated footballs is to compare their rate of fumbles with the rates of other NFL teams. It is important to note that prior to 2007, teams were not permitted to prepare their own footballs before a game-so it was only after that time that such an advantage should be observed -if there actually was such an advantage. Below, are the actual fumble rates for the 23 NFL teams who, like the Patriots, play in a NON-domed stadium where weather conditions that affect fumbles can vary over the course of a season. Each score represents a fumble rate for the team that is averaged over the 7 seasons BEFORE teams were allowed to prepare their own footballs (2000-2006). The number represents the rate of fumbles as a function of the total number of "touches" that an offense had on the ball. So a score of say, “35" would mean that on the average of those 7 seasons, a team fumbled one time for every 35 touches on the ball. A “touch" is defined as a unique player coming into contact with the ball during a play. On a conventional hand-off or pass to one receiver, there are two touches because two players touched the ball. Here are the fumble rates for 2000-2006(Note: these are real fumble numbers. These data are not invented for this assignment. 36,36,36,36,38,38,38,38,40,40,42,42,42,42,44,44,44,46,46,46,46,48,56. During this time period, the New England Patriots fumbled the ball one time for every 42 touches. Conduct a z-test that tests whether it is reasonable to think that the Patriots had no particular competitive advantage on fumbling during the time period 2000-2006.

You may recall that in recent National Football League history, Tom Brady and the New England Patriots were accused of deliberately deflating footballs in order to give themselves a competitive advantage on the football playing field. Presumably, one advantage of playing with a deflated football is that the ball is easier to grip..not only for the quarterback but for everyone who touches it. If the ball is easier to grip, players would fumble it less often. So, one way to examine if the Patriots actually had a competitive advantage due to deflated footballs is to compare their rate of fumbles with the rates of other NFL teams. It is important to note that prior to 2007, teams were not permitted to prepare their own footballs before a game-so it was only after that time that such an advantage should be observed -if there actually was such an advantage. Below, are the actual fumble rates for the 23 NFL teams who, like the Patriots, play in a NON-domed stadium where weather conditions that affect fumbles can vary over the course of a season. Each score represents a fumble rate for the team that is averaged over the 7 seasons BEFORE teams were allowed to prepare their own footballs (2000-2006). The number represents the rate of fumbles as a function of the total number of "touches" that an offense had on the ball. So a score of say, “35" would mean that on the average of those 7 seasons, a team fumbled one time for every 35 touches on the ball. A “touch" is defined as a unique player coming into contact with the ball during a play. On a conventional hand-off or pass to one receiver, there are two touches because two players touched the ball. Here are the fumble rates for 2000-2006(Note: these are real fumble numbers. These data are not invented for this assignment. 36,36,36,36,38,38,38,38,40,40,42,42,42,42,44,44,44,46,46,46,46,48,56. During this time period, the New England Patriots fumbled the ball one time for every 42 touches. Conduct a z-test that tests whether it is reasonable to think that the Patriots had no particular competitive advantage on fumbling during the time period 2000-2006.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section: Chapter Questions
Problem 1RP: Although Pythagoras preceded William Shakespeare by 2,000 years, the philosophy of the Pythagoreans...
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You may recall that in recent National Football League history, Tom Brady and the New England Patriots were accused of deliberately deflating footballs in order to give themselves a competitive advantage on the football playing field. Presumably, one advantage of playing with a deflated football is that the ball is easier to grip...not only for the quarterback but for everyone who touches it. If the ball is easier to grip, players would fumble it less often. So, one way to examine if the Patriots actually had a competitive advantage due to deflated footballs is to compare their rate of fumbles with the rates of other NFL teams. It is important to note that prior to 2007, teams were not permitted to prepare their own footballs before a game-so it was only after that time that such an advantage should be observed -if there actually was such an advantage. Below, are the actual fumble rates for the 23 NFL teams who, like the Patriots, play in a NON-domed stadium where weather conditions that affect fumbles can vary over the course of a season. Each score represents a fumble rate for the team that is averaged over the 7 seasons BEFORE teams were allowed to prepare their own footballs (2000-2006). The number represents the rate of fumbles as a function of the total number of "touches" that an offense had on the ball. So a score of say, "35" would mean that on the average of those 7 seasons, a team fumbled one time for every 35 touches on the ball. A "touch" is defined as a unique player coming into contact with the ball during a play. On a conventional hand-off or pass to one receiver, there are two touches because two players touched the ball. Here are the fumble rates for 2000-2006(Note: these are real fumble numbers. These data are not invented for this assignment. 36,36,36,36,38,38,38,38,40,40,42,42,42,42,44,44,44,46,46,46,46,48,56. During this time period, the New England Patriots fumbled the ball one time for every 42 touches. Conduct a z-test that tests whether it is reasonable to think that the Patriots had no particular competitive advantage on fumbling during the time period 2000-2006.
Transcribed Image Text:You may recall that in recent National Football League history, Tom Brady and the New England Patriots were accused of deliberately deflating footballs in order to give themselves a competitive advantage on the football playing field. Presumably, one advantage of playing with a deflated football is that the ball is easier to grip...not only for the quarterback but for everyone who touches it. If the ball is easier to grip, players would fumble it less often. So, one way to examine if the Patriots actually had a competitive advantage due to deflated footballs is to compare their rate of fumbles with the rates of other NFL teams. It is important to note that prior to 2007, teams were not permitted to prepare their own footballs before a game-so it was only after that time that such an advantage should be observed -if there actually was such an advantage. Below, are the actual fumble rates for the 23 NFL teams who, like the Patriots, play in a NON-domed stadium where weather conditions that affect fumbles can vary over the course of a season. Each score represents a fumble rate for the team that is averaged over the 7 seasons BEFORE teams were allowed to prepare their own footballs (2000-2006). The number represents the rate of fumbles as a function of the total number of "touches" that an offense had on the ball. So a score of say, "35" would mean that on the average of those 7 seasons, a team fumbled one time for every 35 touches on the ball. A "touch" is defined as a unique player coming into contact with the ball during a play. On a conventional hand-off or pass to one receiver, there are two touches because two players touched the ball. Here are the fumble rates for 2000-2006(Note: these are real fumble numbers. These data are not invented for this assignment. 36,36,36,36,38,38,38,38,40,40,42,42,42,42,44,44,44,46,46,46,46,48,56. During this time period, the New England Patriots fumbled the ball one time for every 42 touches. Conduct a z-test that tests whether it is reasonable to think that the Patriots had no particular competitive advantage on fumbling during the time period 2000-2006.
a. State the NULL hypothesis b. State the ALTERNATIVE hypothesis c. Compute the value of the test statistic (z). d. Specify the critical value of "z" needed to reject the null hypothesis e. Decide whether you accept or reject the null hypothesis f. State your conclusion about whether it is reasonable to think that the Patriots had a competitive advantage during this time period. Be clear about the statistical basis/reason for your conclusion.
Transcribed Image Text:a. State the NULL hypothesis b. State the ALTERNATIVE hypothesis c. Compute the value of the test statistic (z). d. Specify the critical value of "z" needed to reject the null hypothesis e. Decide whether you accept or reject the null hypothesis f. State your conclusion about whether it is reasonable to think that the Patriots had a competitive advantage during this time period. Be clear about the statistical basis/reason for your conclusion.
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