Answer:
we can be 95% confident that the true population proportion falls within this interval based on the given sample.
Explanation:
To find the 95% confidence interval for a sample of size 213 with 59.2% successes and a standard error of 0.034, you can use the formula:
Confidence interval = sample proportion ± (critical value * standard error)
Step 1: Calculate the critical value. Since we want a 95% confidence interval, the critical value corresponds to a z-score of 1.96 (which captures 95% of the standard normal distribution).
Step 2: Calculate the margin of error. The margin of error is equal to the critical value multiplied by the standard error. In this case, the margin of error is 1.96 * 0.034 = 0.06664.
Step 3: Calculate the lower bound of the confidence interval. Subtract the margin of error from the sample proportion: 0.592 - 0.06664 = 0.52536.
Step 4: Calculate the upper bound of the confidence interval. Add the margin of error to the sample proportion: 0.592 + 0.06664 = 0.65864.
Therefore, the 95% confidence interval for the sample proportion is (0.52536, 0.65864).
This means that we can be 95% confident that the true population proportion falls within this interval based on the given sample.