Question 2·Medium·Inference from Sample Statistics and Margin of Error
A random sample of 400 town voters were asked whether they plan to vote for Candidate A or Candidate B for mayor. The results, sorted by gender, are shown in the table.
| Plan to vote for Candidate A | Plan to vote for Candidate B | |
|---|---|---|
| Female | 202 | 20 |
| Male | 34 | 144 |
The town has a total of 6,000 voters. Based on the table, what is the best estimate of the number of voters who plan to vote for Candidate A?
For proportion and margin-of-error style questions, first combine the relevant counts from the table to get the total for the group of interest, then divide by the sample size to find the sample proportion. Treat that proportion as representative of the whole population and multiply it by the given total number of individuals. Avoid rounding the proportion too early, and always check that you are using all relevant rows and columns (for example, both genders) rather than just one part of the table.
Hints
Count Candidate A supporters in the sample
Use the table to add the number of female voters who support Candidate A to the number of male voters who support Candidate A.
Turn the count into a proportion
Once you know how many out of the 400 sampled voters support Candidate A, write this as a fraction over 400 and then as a decimal.
Scale up to the full town
Use the proportion from the sample and apply it to the total 6,000 voters. Think about what operation connects a proportion and a total number of voters.
Desmos Guide
Use Desmos to compute the estimate
In Desmos, type (202 + 34) / 400 * 6000 and press Enter. The displayed value is the estimated number of voters in the town who plan to vote for Candidate A.
Step-by-step Explanation
Find how many sampled voters chose Candidate A
From the table:
- Female voters for A: 202
- Male voters for A: 34
Total sampled voters who plan to vote for Candidate A:
So, 236 out of the 400 people in the sample said they would vote for Candidate A.
Find the proportion of the sample that supports Candidate A
The total sample size is 400 voters.
The proportion of the sample who support Candidate A is
Simplify this fraction:
So, about (59%) of the sampled voters support Candidate A.
Apply this proportion to the entire town
Assume the sample is representative of all 6,000 voters.
To estimate how many of the 6,000 voters support Candidate A, multiply the proportion by 6,000:
So, the best estimate of the number of voters in the town who plan to vote for Candidate A is 3540.