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. 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) (0.155, 0.245)
B) (0.162, 0.238)
C) (0.141, 0.259)
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: "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. 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) (0.155, 0.245)
B) (0.162, 0.238)
C) (0.141, 0.259)
D) (0.145, 0.255)

Quizplus · Accepted Answer

The confidence interval for the multinomial probability associated with the "Agree Strongly" response is (0.155, 0.245). This is because the sample size is 300 and the number of Internet users who agree strongly is 60. The formula for the confidence interval is:sample proportion +/- z * sqrt((sample proportion * (1 - sample proportion)) / sample size)where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, z = 1.96. Plugging in the values, we get:0.2 +/- 1.96 * sqrt((0.2 * (1 - 0.2)) / 300)= 0.2 +/- 1.96 * 0.044= 0.2 +/- 0.086= (0.155, 0.245)

Inc Technology Reported the Results of Consumer Survey in Which