Assume that a sample is used to estimate a population proportion p. Find the margin of error. 95% confidence; n = 250, x = 130
To find the margin of error for estimating a population proportion, we can use the formula:
Margin of Error = Critical value * Standard Error
First, we need to find the critical value. For a 95% confidence level, the critical value corresponds to a 2-tailed test.
Using a standard normal distribution table or a calculator, the critical value for a 95% confidence level is approximately 1.96.
Next, we need to calculate the standard error. The formula for the standard error when estimating a population proportion is:
Standard Error = sqrt((p * (1 - p)) / n)
Given that n = 250 and x = 130, we can calculate p by dividing the number of successes (x) by the sample size (n):
p = x / n = 130 / 250 = 0.52
Now, we can calculate the standard error:
Standard Error = sqrt((0.52 * (1 - 0.52)) / 250) ≈ 0.035
Finally, we can calculate the margin of error by multiplying the critical value by the standard error:
Margin of Error = 1.96 * 0.035 ≈ 0.0684
Therefore, the margin of error is approximately 0.0684.