A Multinomial Experiment with K = 4 Cells and N $\begin{array} { r | r r r r } & { \text { Cell } } \\& 1 & 2 & 3 & 4 \\\hline \mathrm { n } _ { \mathrm { i } } & 65 & 69 & 80 & 86\end{array}$

question 34

Essay

A multinomial experiment with k = 4 cells and n = 300 produced the data shown in the following table. $\begin{array} { r | r r r r } & { \text { Cell } } \\& 1 & 2 & 3 & 4 \\\hline \mathrm { n } _ { \mathrm { i } } & 65 & 69 & 80 & 86\end{array}$

Do these data provide sufficient evidence to contradict the null hypothesis that $\mathrm { p } _ { 1 } = 0.20$ , $\mathrm { p } _ { 2 } = 0.20$ , $\mathrm { p } _ { 3 } = 0.30$ , and $\mathrm { p } _ { 4 } = 0.30$ ? Test using $\alpha = 0.05$ .

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Definitions:

Expressive Aphasia

A neurological condition characterized by the impaired ability to produce language, despite often retaining comprehension abilities.

Stroke

A medical condition where poor blood flow to the brain results in cell death, leading to potential loss of functions such as movement or speech.

Afferent Neurons

Nerve cells that carry sensory information from the body's periphery towards the central nervous system.

Efferent Neurons

Nerve cells that carry neural impulses away from the central nervous system to effectors such as muscles and glands.