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Consider a Multinomial Experiment Involving 100 Trials and 3 Categories

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Consider a multinomial experiment involving 100 trials and 3 categories (cells). The observed frequencies resulting from the experiment are shown in the accompanying table.
Consider a multinomial experiment involving 100 trials and 3 categories (cells). The observed frequencies resulting from the experiment are shown in the accompanying table.     Use the 5% significance level to test the hypotheses H <sub>0</sub>: p <sub>1</sub> = 0.45, p <sub>2</sub> = 0.30, p <sub>3</sub> = 0.25 vs. H <sub>1</sub>: At least two proportions differ from their specified values. Use the 5% significance level to test the hypotheses H 0: p 1 = 0.45, p 2 = 0.30, p 3 = 0.25 vs. H 1: At least two proportions differ from their specified values.


Definitions:

Personal Judgments

Opinions or decisions formed by individuals based on personal feelings, tastes, or opinions, often without external input or influence.

Certainty

The state of being confident and free from doubt about something, often implying a high degree of belief in the accuracy or truth of an outcome or fact.

Fully Informed

Being fully informed means having all the necessary and relevant information or knowledge about a particular subject or situation before making decisions.

Objective Probability

A measure of the likelihood of an event occurring, based on factual data and statistical analysis rather than personal judgment.

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