Consider a Multinomial Experiment Involving 100 Trials and 4 Categories

question 78

Essay

Consider a multinomial experiment involving 100 trials and 4 categories (cells). The observed frequencies resulting from the experiment are shown in the accompanying table. $$\begin{array} { | l | c | c | c | c | } \hline \text { Category } & 1 & 2 & 3 & 4 \\\hline \text { Frequency } & 18 & 30 & 25 & 27 \\\hline\end{array}$$ Use the 5% significance level to test the hypotheses.
H₀ : p₁ = 0.25, p₂ = 0.30, p₃ = 0.20, p₄ = 0.25.
H₁ ;At least two proportions differ from their specified values.

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Definitions:

Finite Population Correction

A statistical adjustment made when the sample size is a significant fraction of the total population, reducing variance estimates to prevent overestimation.

Standard Error

Standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.

Estimate

An approximation or educated guess based on available data or evidence.

Mean

The average of a set of values, calculated by dividing the sum of these values by their count.