Which of the following could be an appropriate alternative hypothesis for a statistical test concerning the mean income of 17-year old males?
A) $H _ { 1 } : \bar { X } = \$ 2617$
B) $H _ { 1 : } \mu = \$ 2617$
C) $H _ { 1 } : \bar { X } \neq \$ 2617$
D) $H _ { 1 } : \mu \neq \$ 2617$

Question

Which of the following could be an appropriate alternative hypothesis for a statistical test concerning the mean income of 17-year old males? 
A) $H _ { 1 } : \bar { X } = \$ 2617$
B) $H _ { 1 : } \mu = \$ 2617$
C) $H _ { 1 } : \bar { X } \neq \$ 2617$
D) $H _ { 1 } : \mu \neq \$ 2617$

Quizplus · Accepted Answer

Choice D is the only option that correctly states the alternative hypothesis for a statistical test concerning the mean income of 17-year old males. The null hypothesis would typically be that the mean income is equal to some value (e.g. the national average), and the alternative hypothesis would be that the mean income is either higher or lower than that value. The use of the symbol $\mu$ (the population mean) is also appropriate here, as opposed to $\bar{X}$ (the sample mean), since we are likely interested in making inferences about the entire population of 17-year old males, not just the ones in our sample.

Which of the Following Could Be an Appropriate Alternative Hypothesis H1:Xˉ=$2617H _ { 1 } : \bar { X } = \$ 2617H1​:Xˉ=$2617

Which of the Following Could Be an Appropriate Alternative Hypothesis $H _ { 1 } : \bar { X } = \$ 2617$