## Related questions with answers

Football owners are constantly in competition for good players. The more wins, the more possible that the team will provide good business returns for the owners. The resources that each of the 32 teams has in the National Football League (NFL) vary, but the draft system is designed to counteract the advantages that wealthier teams may have. Is it working or does the size of the payroll matter? Here is the regression output for the 2012/2013 season between the team payroll and the number of wins.

$\begin{array}{lllll}\text { Predictor } & \text{Coeff} & \text{ SE(Coeff) } & \text{ t-Value}& \text{ P-Value}\end{array}$

$\begin{array}{lllll}\text { Intercept } & -16.31846 & 8.49246 & -1.922 & 0.06421\end{array}$

$\begin{array}{lrrrr}\text{ Payroll(\$M) } & 0.21875 & 0.07636 & 2.865 & 0.00755\end{array}$

$s=2.779 \quad R-S q=21.48 \%$

b) Conduct the hypothesis test and state your conclusion in context.

Solution

VerifiedIn this problem, we want to perform a **hypothesis test** to determine whether there is a **linear association** between the size of the **Payroll** of the football players and the team's number of **Wins** given the *computer output* of the regression analysis as shown below:

$\small \text{Figure $1$. Given Computer Regression Analysis Table}$

where it was determined that the number of **Wins** is the **response/dependent variable** $(y)$ and the size of the **Payroll (in $\$1,000,000$)** is the **independent variable** $(x)$.

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