A Multinomial Experiment With $k = 3$ Cells And $n = 100$

question 23

Essay

A multinomial experiment with $k = 3$ cells and $n = 100$ has been conducted and the results are shown in the table.
$\begin{array}{l}\quad\quad\text { Cell }\\\begin{array} { c | c c c } & 1 & 2 & 3 \\\hline n _ { i } & 46 & 32 & 22\end{array}\end{array}$
Construct a 99% confidence interval for the multinomial probability associated with cell 2.

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Definitions:

Oldest Regions

refers to the most ancient parts of the brain, such as the brainstem and cerebellum, which govern fundamental life functions like breathing, heart rate, and motor coordination.

Breathing

The process of taking air into and expelling it from the lungs, vital for the exchange of oxygen and carbon dioxide.

Highly Aroused

A state of heightened physiological activity, often associated with increased readiness or alertness.

Reticular Formation

A network of nerve pathways in the brainstem involved in consciousness, the sleep-wake cycle, and filtering incoming stimuli to discriminate irrelevant background stimuli.