Which of the following would be an appropriate alternative hypothesis for the one-sample t test of the hypothesis that the mean reaction time of a population of 45 year-old drivers is 0.653 seconds?
A) $H _ { 1 } : \bar { X } = 0.653$
B) $H _ { 1 } : \bar { X } \neq 0.653$
C) $H _ { 1 } : \mu = 0.653$
D) $H _ { 1 } : \mu \neq 0.653$

Question

Which of the following would be an appropriate alternative hypothesis for the one-sample t test of the hypothesis that the mean reaction time of a population of 45 year-old drivers is 0.653 seconds? 
A) $H _ { 1 } : \bar { X } = 0.653$
B) $H _ { 1 } : \bar { X } \neq 0.653$
C) $H _ { 1 } : \mu = 0.653$
D) $H _ { 1 } : \mu \neq 0.653$

Quizplus · Accepted Answer

The alternative hypothesis should always state any deviation from the null hypothesis. In this case, the null hypothesis is that the mean reaction time is 0.653 seconds. Therefore, the alternative hypothesis should state any deviation from this value, which is option D, $H _ { 1 } : \mu \neq 0.653$. Options A and C only repeat the null hypothesis, and option B is too vague since it does not specify a direction of deviation.

Which of the Following Would Be an Appropriate Alternative Hypothesis H1:Xˉ=0.653H _ { 1 } : \bar { X } = 0.653H1​:Xˉ=0.653

Which of the Following Would Be an Appropriate Alternative Hypothesis $H _ { 1 } : \bar { X } = 0.653$