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Chi-Squared Values and $p$-values

APSTAT-VFEX12

A ${ \chi }^{ 2 }$ test for homogeneity of populations was conducted using data found in a two-way table consisting of $6$ rows and $3$ columns. The ${ \chi }^{ 2 }$ value was found to be $19.63$.

What can we conclude about the results of this test?

A

Since $p = 0.033$, we have strong evidence to suggest that the distribution of proportions is not the same for each of the different populations.

B

Since $p = 0.354$, we do not have enough evidence to suggest that the distribution of proportions is not the same for each of the different populations.

C

Since $p = 19.63$, we do not have any evidence to suggest that the distribution of proportions is not the same for each of the different populations.

D

Since $p < 0.05$, we have strong evidence that the populations are independent of each other.

E

Since $p > 0.05$, we cannot conclude that the populations are independent of each other.