Asked by Jayson Sta Cruz on Jul 16, 2024
Verified
We are interested in conducting a study to determine the percentage of voters of a state would vote for the incumbent governor.What is the minimum sample size needed to estimate the population proportion with a margin of error of .05 or less at 95% confidence?
A) 200.
B) 100.
C) 58.
D) 385.
Sample Size
The number of observations or elements selected from a population to study a particular property.
Population Proportion
Population proportion represents the fraction or percentage of members in a population that exhibits a particular attribute or characteristic.
Margin of Error
A statistic expressing the amount of random sampling error in a survey's results, indicating the range within which the true value lies with a certain level of confidence.
- Acquire insight into the relationship between sample size and margin of error in the context of interval estimation.
Verified Answer
JH
Jessica HernandezJul 16, 2024
Final Answer :
D
Explanation :
The formula to calculate the minimum sample size needed is:
n = (z^2 * p * q) / E^2
where:
z = z-score (from z-table) for 95% confidence level = 1.96
p = estimated proportion (we can use 0.5 as it gives maximum sample size)
q = 1-p
E = margin of error = 0.05
Substituting these values in the formula:
n = (1.96^2 * 0.5 * 0.5) / 0.05^2
n = 384.16
Taking the ceiling of the value, the minimum required sample size is 385. Therefore, the best choice is D.
n = (z^2 * p * q) / E^2
where:
z = z-score (from z-table) for 95% confidence level = 1.96
p = estimated proportion (we can use 0.5 as it gives maximum sample size)
q = 1-p
E = margin of error = 0.05
Substituting these values in the formula:
n = (1.96^2 * 0.5 * 0.5) / 0.05^2
n = 384.16
Taking the ceiling of the value, the minimum required sample size is 385. Therefore, the best choice is D.
Learning Objectives
- Acquire insight into the relationship between sample size and margin of error in the context of interval estimation.