While conducting a goodness-of-fit test if the observed and expected values are close, you would expect which of the following:
A) Small $\chi ^ { 2 }$ value, large $P$-value
B) Large $\chi ^ { 2 }$ value, large $P$-value
C) Small $\chi ^ { 2 }$ value, small $P$-value
D) Large $\chi ^ { 2 }$ value, small $P$-value

Question

While conducting a goodness-of-fit test if the observed and expected values are close, you would expect which of the following: 
A) Small $\chi ^ { 2 }$ value, large $P$-value
B) Large $\chi ^ { 2 }$ value, large $P$-value
C) Small $\chi ^ { 2 }$ value, small $P$-value
D) Large $\chi ^ { 2 }$ value, small $P$-value

Quizplus · Accepted Answer

A small $\chi ^ { 2 }$ value and a large $P$-value indicate that the observed values are similar to the expected values and the null hypothesis (that the observed values fit the expected values) cannot be rejected. This is what would be expected if the observed and expected values are close.

While Conducting a Goodness-Of-Fit Test If the Observed and Expected χ2\chi ^ { 2 }χ2

While Conducting a Goodness-Of-Fit Test If the Observed and Expected $\chi ^ { 2 }$