Question

Three sample surveys are taken about an upcoming election. In the first sample, 65 out of 80 people plan to vote. In the second sample, 77 out of 100 people plan to vote. In the third sample, 28 out of 35 people plan to vote. To the nearest percent, what is the best estimate of the percentage of people who plan to vote in the upcoming election based on the sample surveys?(1 point)
%

Answer 1

To estimate the percentage of people who plan to vote based on the three surveys, we first calculate the proportion of people in each sample who plan to vote, and then find the weighted average based on the sample sizes.

1. **First sample**:
\[
\text{Proportion} = \frac{65}{80} = 0.8125
\]

2. **Second sample**:
\[
\text{Proportion} = \frac{77}{100} = 0.77
\]

3. **Third sample**:
\[
\text{Proportion} = \frac{28}{35} = 0.8
\]

Next, we should multiply each proportion by the number of respondents in each sample to find the number of people planning to vote from each sample.

- For the first sample:
\[
65 \text{ (people planning to vote)}
\]

- For the second sample:
\[
77 \text{ (people planning to vote)}
\]

- For the third sample:
\[
28 \text{ (people planning to vote)}
\]

Next, we find the total number of respondents across all samples:
\[
80 + 100 + 35 = 215
\]

Now we add the number of people planning to vote from each sample:
\[
65 + 77 + 28 = 170
\]

Lastly, we calculate the overall proportion of people who plan to vote:
\[
\text{Overall proportion} = \frac{170}{215} \approx 0.7907
\]

To convert this to a percentage:
\[
0.7907 \times 100 \approx 79.07\%
\]

Rounding to the nearest percent, the best estimate of the percentage of people who plan to vote in the upcoming election is:
\[
\boxed{79} \%
\]