One May Wish to Test $H _ { 0 } : p _ { 1 } = p _ { 10 } , \ldots , p _ {\alpha } = p _ { \alpha 0 } \text { versus } H _ {\pm } : H _ { 0 }$

Short Answer

One may wish to test $H _ { 0 } : p _ { 1 } = p _ { 10 } , \ldots , p _ {\alpha } = p _ { \alpha 0 } \text { versus } H _ {\pm } : H _ { 0 }$ is not true. The null hypothesis is __________ hypothesis in the sense that each $p _ { 10 }$ is a specified number, so that the expected cell counts when $H _ { 0 }$ is true are uniquely determined numbers.