Final answer:
To calculate the margin of error for a population proportion with a 95% confidence level and a sample size of 10,000 with 40% successes, use the formula E = Z * sqrt[ (p * (1 - p)) / n ], where Z is 1.96. The calculated margin of error E is 0.009604, which rounds to 0.0096.
Step-by-step explanation:
To find the margin of error E for a population proportion p with a 95% confidence level, given a sample size of 10,000 with 40% successes, you use the formula for the confidence interval of a population proportion:
E = Z * √[ (p * (1 - p)) / n ]
Where:
E is the margin of error
Z is the Z-score corresponding to the confidence level
p is the sample proportion (0.40 in this case)
n is the sample size (10,000)
For a 95% confidence level, the Z-score is approximately 1.96. Plugging the values into the formula:
E = 1.96 * √[ (0.40 * (1 - 0.40)) / 10,000 ]
E = 1.96 * √(0.24 / 10,000)
E = 1.96 * √(0.000024)
E = 1.96 * 0.0049
E = 0.009604, which when rounded to four decimal places is 0.0096.