The football coach at State University wishes to determine if there is a change in offensive production between the first half and the second half of his team's recent games. The table below shows the first-half and second-half offensive production (measured in total yards gained per half) for the past six games.
$\begin{array}{lcccccc}\hline & {\text { Game }} \\& 1 & 2 & 3 & 4 & 5 & 6 \\\text { First half yards } & 123 & 136 & 130 & 134 & 95 & 93 \\\text { Second half yards } & 103 & 120 & 116 & 143 & 62 & 60 \\\hline\end{array}$

State the null and alternative hypotheses.

Question

The football coach at State University wishes to determine if there is a change in offensive production between the first half and the second half of his team's recent games. The table below shows the first-half and second-half offensive production (measured in total yards gained per half) for the past six games.
 $\begin{array}{lcccccc}
\hline & {\text { Game }} \
& 1 & 2 & 3 & 4 & 5 & 6 \
\text { First half yards } & 123 & 136 & 130 & 134 & 95 & 93 \
\text { Second half yards } & 103 & 120 & 116 & 143 & 62 & 60 \
\hline
\end{array}$

State the null and alternative hypotheses.
A) $H _ { 0 } : \mu d = 0 , H _ { 1 } : \mu d > 0$
B) $H _ { 0 } : \mu d = 0 , H _ { 1 } \mu d \neq 0$
C) $H _ { 0 } : \mu d = 0 , H _ { 1 } : \mu d < 0$
D) $H _ { 0 } : \mu d = 0 , H _ { 1 } : \mu d = 17.8$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) typically states that there is no effect or no difference, which in this context means no change in offensive production between the first half and the second half ($\mu d = 0$). The alternative hypothesis ($H_1$) should cover all other possibilities except the null, which means it should state that there is a difference ($\mu d \neq 0$), without specifying the direction of the difference.

The Football Coach at State University Wishes to Determine If