A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, "What make of car (U.S., Europe, or Japan) do you drive?" The responses (number in each category) for a sample of 100 entrepreneurs are summarized below. The goal of the analysis is to determine if the proportions of entrepreneurs who drive American, European, and Japanese cars differ.

$$\begin{array} { c c c }
\text { U.S. } & \text { Europe } & \text { Japan } \
\hline 40 & 35 & 25 \
\hline
\end{array}$$
In order to determine whether the true proportions 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 "Europe" response was desired. Which of the following
Confidence intervals should be used?

Question

A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, "What make of car (U.S., Europe, or Japan) do you drive?" The responses (number in each category) for a sample of 100 entrepreneurs are summarized below. The goal of the analysis is to determine if the proportions of entrepreneurs who drive American, European, and Japanese cars differ.

$$\begin{array} { c c c } 
\text { U.S. } & \text { Europe } & \text { Japan } \
\hline 40 & 35 & 25 \
\hline
\end{array}$$
 In order to determine whether the true proportions 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 "Europe" response was desired. Which of the following
Confidence intervals should be used?

Quizplus · Accepted Answer

The confidence interval for the multinomial probability associated with the "Europe" response is (0.257, 0.443). This is because the sample size is 100 and the number of entrepreneurs who drive European cars is 35. The formula for the confidence interval is:p ± z * sqrt((p * (1 - p)) / n)where p is the sample proportion, z is the z-score for the desired confidence level, and n is the sample size.For a 95% confidence level, the z-score is 1.96. Plugging in the values, we get:0.35 ± 1.96 * sqrt((0.35 * (1 - 0.35)) / 100)= 0.35 ± 1.96 * sqrt((0.35 * 0.65) / 100)= 0.35 ± 1.96 * sqrt(0.002275)= 0.35 ± 1.96 * 0.0477= 0.35 ± 0.093= (0.257, 0.443)

A Survey of Entrepreneurs Focused on Their Job Characteristics, Work U.S. Europe Japan 403525\begin{array} { c c c } \text { U.S. } & \text { Europe } & \text { Japan } \\\hline 40 & 35 & 25 \\\hline\end{array} U.S. 40​ Europe 35​ Japan 25​​

A Survey of Entrepreneurs Focused on Their Job Characteristics, Work $\begin{array} { c c c } \text { U.S. } & \text { Europe } & \text { Japan } \\\hline 40 & 35 & 25 \\\hline\end{array}$