A research company wants to poll a sample of 100 registered ✓ Solved

A research company wants to poll a sample of 100 registered voters in a small town. There are 345 registered republicans, 452 registered democrats, and 510 registered voters for neither party. How many voters from each group should the company poll if it wants a stratified sample?

Paper For Above Instructions

Stratified sampling is a method used to improve the representation of different subgroups within a population. In this case, the research company wants to poll registered voters from three distinct groups: Republicans, Democrats, and those with neither affiliation. To determine how many voters to poll from each group in a stratified sample, we first need to understand the proportions of each group relative to the total population of registered voters.

Population Breakdown

In the small town, we have the following data:

  • Registered Republicans: 345

  • Registered Democrats: 452

  • Registered Voters for Neither Party: 510

The total number of registered voters can be calculated as follows:

Total Registered Voters: 345 + 452 + 510 = 1307

Determining Sample Sizes

To achieve a stratified sample, we represent each group according to its proportion of the total population. The sample size is set to 100 voters, and we can calculate the number of voters to be polled from each group using the formula:

Sample Size for Group = (Group Size / Total Registered Voters) × Sample Size

For Registered Republicans:

Sample Size: (345 / 1307) × 100 ≈ 26.4 ≈ 26 voters

For Registered Democrats:

Sample Size: (452 / 1307) × 100 ≈ 34.6 ≈ 35 voters

For Registered Voters for Neither Party:

Sample Size: (510 / 1307) × 100 ≈ 39.0 ≈ 39 voters

Final Counts

Based on the calculations above, the research company should poll the following number of voters to achieve a stratified sample:

  • Republicans: 26 voters

  • Democrats: 35 voters

  • Neither Party: 39 voters

Conclusion

This approach ensures that each subgroup is adequately represented in the poll, thereby increasing the reliability and validity of the findings.

References

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