A multinomial experiment with k = 4 cells and n = 300 produced the data shown in the
following table.

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 $\alpha = .05$.

Question

A multinomial experiment with k = 4 cells and n = 300 produced the data shown in the
following table.

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 $\alpha = .05$.

Quizplus · Accepted Answer

The Answer is Since

\chi ^ { 2 } = 3.056 < \chi _ { .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 Cells and N p1=.20,p2=.20,p3=.30p _ { 1 } = .20 , p _ { 2 } = .20 , p _ { 3 } = .30p1​=.20,p2​=.20,p3​=.30

A Multinomial Experiment with K = 4 Cells and N $p _ { 1 } = .20 , p _ { 2 } = .20 , p _ { 3 } = .30$