A multinomial experiment with $\mathrm { k } = 4$ cells and $\mathrm { n } = 300$ produced the data shown in the following table.

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

Question

A multinomial experiment with $\mathrm { k } = 4$ cells and $\mathrm { n } = 300$ produced the data shown in the following table.

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

Quizplus · Accepted Answer

The Answer is Since

\chi ^ { 2 } = 3.056 < x _ { 0.05 } ^ { 2 } = 7.815 ( \mathrm { df } = 3 )

, we do not reject the null hypothesis. There is not sufficient evidence that the cell proportions differ from those given in the null hypothesis.

A Multinomial Experiment With k=4\mathrm { k } = 4k=4 Cells And

A Multinomial Experiment With $\mathrm { k } = 4$ Cells And