The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. $$\begin{array} { l l }
\text { Political Party } & \text { Support } \
\text { Democrats } & 100 \
\text { Republicans } & 120 \
\text { Independents } & 80
\end{array}$$ We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.The calculated value for the test statistic equals
A) 2.
B) 4.
C) 0.
D) 8.

Question

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. $$\begin{array} { l l } 
\text { Political Party } & \text { Support } \
\text { Democrats } & 100 \
\text { Republicans } & 120 \
\text { Independents } & 80
\end{array}$$  We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.The calculated value for the test statistic equals
A) 2.
B) 4.
C) 0.
D) 8.

Quizplus · Accepted Answer

The expected frequency for each group, if uniformly distributed, would be 100 (300 total / 3 groups). The test statistic is calculated using the formula for chi-square: $\sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. Calculating for each group: Democrats: $(100-100)^2/100 = 0$, Republicans: $(120-100)^2/100 = 4$, Independents: $(80-100)^2/100 = 4$. Summing these gives a test statistic of 8.

The Following Table Shows the Number of Individuals in a Sample