Rounded to three decimal places, the margin of error for a 95% confidence interval based on the given sample proportion and size is approximately 0.122.
To determine the margin of error for a confidence interval based on a sample proportion, you'd typically use the form
Margin of Error=Z× √p(1−p)/n
Where:
Z is the Z-score corresponding to the desired level of confidence.
p is the sample proportion.
n is the sample size.
The Z-score is determined based on the desired confidence level. For example, if you're aiming for a 95% confidence level, the Z-score would be approximately 1.96.
Given:
Sample proportion,
p=57.14%=0.5714
Sample size,
n=63
Assuming a 95% confidence level, the Z-score is approximately 1.96.
Now, plug in these values into the formula:
Margin of Error=1.96× √0.5714×(1−0.5714)/63
Let's calculate:
Margin of Error≈1.96×√0.5714×0.4286/ 63
Margin of Error≈1.96×√ 0.24487724/63
Margin of Error≈1.96× √0.003889476
Margin of Error≈1.96×0.062385627
Margin of Error≈0.122101076
Rounded to three decimal places, the margin of error for a 95% confidence interval based on the given sample proportion and size is approximately 0.122.