When testing the hypothesis $H _ { o } : p _ { 1 } - p _ { 2 } = 0$, the alternative hypotheses $H _ { a } : p _ { 1 } - p _ { 2 } 0$ and $H _ { a } : p _ { 2 } - p _ { 1 } 0$ can be used interchangeably.

Question

When testing the hypothesis $H _ { o } : p _ { 1 } - p _ { 2 } = 0$, the alternative hypotheses $H _ { a } : p _ { 1 } - p _ { 2 } > 0$ and $H _ { a } : p _ { 2 } - p _ { 1 } > 0$ can be used interchangeably.

Quizplus · Accepted Answer

The alternative hypotheses $H _ { a } : p _ { 1 } - p _ { 2 } > 0$ and $H _ { a } : p _ { 2 } - p _ { 1 } > 0$ are not interchangeable because they represent different directions of the effect being tested.

When Testing the Hypothesis Ho:p1−p2=0H _ { o } : p _ { 1 } - p _ { 2 } = 0Ho​:p1​−p2​=0

When Testing the Hypothesis $H _ { o } : p _ { 1 } - p _ { 2 } = 0$