Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: ʺThe government needs to be able to scan
Internet messages and user communications to prevent fraud and other crimes.ʺ The possible
Responses were ʺagree stronglyʺ, ʺagree somewhatʺ, ʺdisagree somewhatʺ, and ʺdisagree stronglyʺ.
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. As part of that analysis, a $95 \%$ confidence interval for the multinomial probability associated with the "Agree Strongly" response was desired. Which of the following confidence intervals should be used?
A) $( 0.141,0.259 )$
B) $( 0.162,0.238 )$
C) $( 0.155,0.245 )$
D) $( 0.145,0.255 )$

Question

Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: ʺThe government needs to be able to scan
Internet messages and user communications to prevent fraud and other crimes.ʺ The possible
Responses were ʺagree stronglyʺ, ʺagree somewhatʺ, ʺdisagree somewhatʺ, and ʺdisagree stronglyʺ.
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. As part of that analysis, a $95 \%$ confidence interval for the multinomial probability associated with the "Agree Strongly" response was desired. Which of the following confidence intervals should be used?
A) $( 0.141,0.259 )$
B) $( 0.162,0.238 )$
C) $( 0.155,0.245 )$
D) $( 0.145,0.255 )$

Quizplus · Accepted Answer

The confidence interval for the proportion of "Agree Strongly" responses, which is 60 out of 300, or 0.2, can be calculated using the formula for a confidence interval for a proportion. The correct interval, given the choices, that encompasses the proportion 0.2 (20%) with a reasonable margin for error, considering a 95% confidence level and the sample size, is $(0.155, 0.245)$. This interval is the only one that centers around 0.2 and provides a plausible range for the true proportion of "Agree Strongly" responses in the population, considering the standard error and the Z-score for a 95% confidence level.

Inc Technology Reported the Results of Consumer Survey in Which