A Multinomial Experiment With $k = 4$ Cells And $n = 300$

question 45

Essay

A multinomial experiment with $k = 4$ cells and $n = 300$ produced the data shown in the following table.
$\begin{array} { l | r r r r } &\text { Cell } \\& 1 & 2 & 3 & 4 \\\hline n _ { i } & 65 & 69 & 80 & 86\end{array}$
Do these data provide sufficient evidence to contradict the null hypothesis that $p _ { 1 } = .20 , p _ { 2 } = .20 , p _ { 3 } = .30$ , and $p _ { 4 } = .30$ ? Test using $\alpha = .05$ .

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