Among all the respondents, what is the relative frequency of those who are Democrat and opposed to the bill? Round your answer to two decimal places.
Understand the Problem
The question asks for the relative frequency of respondents who identify as Democrats and are opposed to a specific bill. To solve this, we will calculate the proportion of Democrats who opposed the bill from the total number of respondents surveyed.
Answer
The relative frequency of those who are Democrat and opposed to the bill is $0.17$.
Answer for screen readers
The relative frequency of those who are Democrat and opposed to the bill is $0.17$.
Steps to Solve
- Identify the necessary values from the table
From the contingency table, we look for the number of Democrats who are opposed to the bill. According to the table, this number is 43.
- Calculate the total number of Democrats
To find the total number of Democrats, we add the values in the "In favor of," "Opposed to," and "Indifferent to" columns for Democrats: $$ 24 + 43 + 17 = 84 $$
- Calculate the relative frequency
The relative frequency of those who are Democrats and opposed to the bill is calculated by dividing the number of Democrats opposed (43) by the total number of respondents (257): $$ \text{Relative Frequency} = \frac{43}{257} $$
- Perform the division
Now, we calculate the value: $$ \frac{43}{257} \approx 0.1677 $$
- Round to two decimal places
Finally, rounding 0.1677 to two decimal places, we get: $$ 0.17 $$
The relative frequency of those who are Democrat and opposed to the bill is $0.17$.
More Information
The relative frequency measures how often a specific category occurs within the total population. In this case, it shows that approximately 17% of the respondents identify as Democrats and are opposed to the bill.
Tips
- Failing to sum the categories correctly when calculating the total number of Democrats.
- Not rounding the final answer to two decimal places as required.
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