Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table.
$\begin{array}{l|l}
\text { RESPONSE } & \text { NUMBER } \
\hline \text { Agree Strongly } & 60 \
\text { Agree Somewhat } & 110 \
\text { Disagree Somewhat } & 80 \
\text { Disagree Strongly } & 50
\end{array}$

In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. Calculate the value of the test statistic for the desired analysis.
A) $\chi ^ { 2 } = 28.0$
B) $\chi ^ { 2 } = 0.25$
C) $\chi ^ { 2 } = 75$
D) $\chi ^ { 2 } = 22.54$

Question

Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. 
$\begin{array}{l|l}
\text { RESPONSE } & \text { NUMBER } \
\hline \text { Agree Strongly } & 60 \
\text { Agree Somewhat } & 110 \
\text { Disagree Somewhat } & 80 \
\text { Disagree Strongly } & 50
\end{array}$

In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. Calculate the value of the test statistic for the desired analysis.
A) $\chi ^ { 2 } = 28.0$
B) $\chi ^ { 2 } = 0.25$
C) $\chi ^ { 2 } = 75$
D) $\chi ^ { 2 } = 22.54$

Quizplus · Accepted Answer

The chi-square test statistic is calculated using the formula $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. Assuming equal expected proportions, $E_i = \frac{300}{4} = 75$ for each category. Calculating for each category and summing gives $\chi^2 = 28.0$.

Inc Technology Reported the Results of Consumer Survey in Which