Consider a Multinomial Experiment Involving 100 Trials and 3 Categories $$\begin{array} { | l | c c c | } \hline \text { Categary } & 1 & 2 & 3 \\\hline \text { Frequency } & 38 & 35 & 27 \\\hline\end{array}$$

question 4

Essay

Consider a multinomial experiment involving 100 trials and 3 categories (cells). The observed frequencies resulting from the experiment are shown in the accompanying table. $$\begin{array} { | l | c c c | } \hline \text { Categary } & 1 & 2 & 3 \\\hline \text { Frequency } & 38 & 35 & 27 \\\hline\end{array}$$ Use the 5% significance level to test the hypotheses H₀: p₁ = 0.45, p₂ = 0.30, p₃ = 0.25 vs. H₁: At least two proportions differ from their specified values.

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Definitions:

Prostate Cancer

A form of cancer that develops in the prostate gland of the male reproductive system, often detected via blood tests or physical examination.

Fecal Impaction

A severe form of constipation where hard stool masses are stuck in the rectum and cannot be expelled.

Rectal Abscess

A collection of pus in the tissue surrounding the rectum, often causing pain and swelling.

Distended Abdomen

An increase in abdominal size, often due to gas, fluid accumulation, or enlargement of abdominal organs.