Final answer:
To estimate the confidence interval for the student's example, calculate the sample proportion and the error bound for the proportion using the z-score for your desired confidence level. Then, add and subtract EBP from the sample proportion to get the confidence interval.
Step-by-step explanation:
To calculate the confidence interval for a population proportion, we can use the sample proportion (p') and the formula for the confidence interval which is given by (p' - EBP, p' + EBP). In this case, the sample size is 263, and we have 142 successes. First, we calculate the sample proportion as p' = x/n, where x is the number of successes, and n is the sample size. Then, we determine the error bound for the proportion (EBP) using the standard error and the z-score for the desired confidence level (often 1.96 for a 95% confidence interval). The formula for EBP is EBP = z * sqrt((p'(1 - p')/n)). After finding p' and EBP, we can then compute the confidence interval.
For our specific example, the sample proportion is p' = 142 / 263 = 0.540. To calculate EBP, we need the z-score for the desired confidence level, which is typically found in a z-table or by using a calculator. Suppose we want a 95% confidence interval; we would use a z-score of approximately 1.96. We would then calculate the standard error, followed by EBP, and finally add and subtract EBP from the sample proportion to find the confidence interval.
Keep in mind, accuracy up to three decimal places is required, so when making the final calculation, ensure to round appropriately.