A Multinomial Experiment with K = 4 Cells and N $\begin{array} { r | r r r r } & { \text { Cell } } \\& 1 & 2 & 3 & 4 \\\hline \mathrm { n } _ { \mathrm { i } } & 65 & 69 & 80 & 86\end{array}$

Essay

A multinomial experiment with k = 4 cells and n = 300 produced the data shown in the following table. $\begin{array} { r | r r r r } & { \text { Cell } } \\& 1 & 2 & 3 & 4 \\\hline \mathrm { n } _ { \mathrm { i } } & 65 & 69 & 80 & 86\end{array}$

Do these data provide sufficient evidence to contradict the null hypothesis that $\mathrm { p } _ { 1 } = 0.20$ , $\mathrm { p } _ { 2 } = 0.20$ , $\mathrm { p } _ { 3 } = 0.30$ , and $\mathrm { p } _ { 4 } = 0.30$ ? Test using $\alpha = 0.05$ .