Questions: A sample of 302 people is surveyed. The people are classified according to political affiliation ("Democrat", "Republican", or "Independent"). They are also classified according to opinion on a bill ("in favor of", "opposed to", or "indifferent to"). The results are given in the contingency table below. In favor of Opposed to Indifferent to ------------------------------------------------------ Democrat 24 28 39 Republican 23 47 47 Independent 34 39 21 What is the relative frequency of respondents who are in favor of the bill? Round your answer to two decimal places.

A sample of 302 people is surveyed. The people are classified according to political affiliation ("Democrat", "Republican", or "Independent"). They are also classified according to opinion on a bill ("in favor of", "opposed to", or "indifferent to"). The results are given in the contingency table below. In favor of Opposed to Indifferent to ------------------------------------------------------ Democrat 24 28 39 Republican 23 47 47 Independent 34 39 21 What is the relative frequency of respondents who are in favor of the bill? Round your answer to two decimal places.
Transcript text: Prep for Week 5 - 10/14-20 - P ALEKS - Eljah Madrid - Leam https://www-awu.aleks.com/alekscgi/x/lsl.exe/1o_u-IgNslkasNW8D8A9PVVREqZGTyQOVKIA8bapKpcZyiCEjvwjFgyvKCL9ysUf8JL1yNsn-VYY... Probability Calculating relative frequencies in a contingency table Elijah Español A sample of 302 people is surveyed. The people are classified according to political affiliation ("Democrat", "Republican", or "Independent"). They are also classified according to opinion on a bill ("in favor of", "opposed to", or "indifferent to"). The results are given in the contingency table below. \begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } & In favor of & Opposed to & Indifferent to \\ \hline Democrat & 24 & 28 & 39 \\ \hline Republican & 23 & 47 & 47 \\ \hline Independent & 34 & 39 & 21 \\ \hline \end{tabular} What is the relative frequency of respondents who are in favor of the bill? Round your answer to two decimal places. $\square$
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Solution

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Solution Steps

Step 1: Total Respondents

The total number of respondents surveyed is given by the sum of all entries in the contingency table:

\[ \text{Total respondents} = 302 \]

Step 2: Total Respondents in Favor

To find the total number of respondents who are in favor of the bill, we sum the entries corresponding to "in favor of" across all political affiliations:

\[ \text{Total respondents in favor} = 24 + 23 + 34 = 81 \]

Step 3: Relative Frequency Calculation

The relative frequency of respondents who are in favor of the bill is calculated by dividing the total number of respondents in favor by the total number of respondents:

\[ \text{Relative frequency} = \frac{\text{Total respondents in favor}}{\text{Total respondents}} = \frac{81}{302} \approx 0.2682 \]

Rounding this value to two decimal places gives:

\[ \text{Relative frequency (rounded)} \approx 0.27 \]

Final Answer

The relative frequency of respondents who are in favor of the bill is

\[ \boxed{0.27} \]

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