Asked by Lauren Oliveira on Jun 12, 2024
Verified
A political party is interested in finding out what kind of popular support they might expect on an environmental initiative.Similar issues have gotten 87% support.The committee will set up a polling program to assure 95% confidence that the margin of error is less than 9%.What sample size will suffice?
A) 162
B) 5
C) 54
D) 48
E) 38
Environmental Initiative
An environmental initiative is a project or program aimed at promoting sustainability, conserving natural resources, reducing pollution, and protecting ecosystems.
Margin of Error
An expression of the amount of random sampling error in a survey's results, indicating the range of accuracy.
Sample Size
The number of individuals or observations included in a sample, which is a subset of a larger population for the purpose of statistical analysis.
- Determine the suitable number of observations needed to reach specified confidence intervals and error margins in surveys and polls.
Verified Answer
NH
Norika HangulaJun 17, 2024
Final Answer :
C
Explanation :
We need to use the formula for sample size calculation for proportions:
n = (z^2 * p * q) / E^2
where:
z = z-score for the level of confidence (95% = 1.96)
p = estimated proportion (87% = 0.87)
q = 1 - p
E = maximum margin of error (9% = 0.09)
Plugging in the values:
n = (1.96^2 * 0.87 * 0.13) / 0.09^2
n = 53.64
n ≈ 54 (rounded up)
Therefore, the best choice is C with a sample size of 54.
n = (z^2 * p * q) / E^2
where:
z = z-score for the level of confidence (95% = 1.96)
p = estimated proportion (87% = 0.87)
q = 1 - p
E = maximum margin of error (9% = 0.09)
Plugging in the values:
n = (1.96^2 * 0.87 * 0.13) / 0.09^2
n = 53.64
n ≈ 54 (rounded up)
Therefore, the best choice is C with a sample size of 54.
Learning Objectives
- Determine the suitable number of observations needed to reach specified confidence intervals and error margins in surveys and polls.