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. State the null and alternative hypotheses. A) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } \mu _ { d } \neq 0$ B) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } : \mu _ { d } 0$ C) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } : \mu d = 37$ D) $H _ { 0 } : \mu d = 0 , H _ { 1 } : \mu d

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.  State the null and alternative hypotheses. 
A) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } \mu _ { d } \neq 0$ 
B) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } : \mu _ { d } > 0$ 
C) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } : \mu d = 37$ 
D) $H _ { 0 } : \mu d = 0 , H _ { 1 } : \mu d < 0$

Quizplus · Accepted Answer

The null hypothesis should state that there is no difference in offensive production between the first and second half of the games, which is represented by $H _ { 0 } : \mu _ { d } = 0$. The alternative hypothesis should state that there is a difference, which can be a two-sided alternative ($H _ { 1 } : \mu _ { d } \neq 0$). Therefore, the best choice is A. Choice B suggests a one-sided alternative indicating that offensive production is greater in the second half, which may not be the case. Choice C suggests a specific value for the difference in means, which is not appropriate for a hypothesis test. Choice D suggests a one-sided alternative indicating that offensive production is less in the second half, which may not be the case.

The Football Coach at State University Wishes to Determine If H0:μd=0,H1μd≠0H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } \mu _ { d } \neq 0H0​:μd​=0,H1​μd​=0

The Football Coach at State University Wishes to Determine If $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } \mu _ { d } \neq 0$