Final answer:
To construct a 99% confidence interval given n = 570 and p-hat = 0.34, use the formula CI = p-hat ± Z * sqrt((p-hat * (1-p-hat)) / n). Determine the critical value Z associated with a 99% confidence level and calculate the confidence interval. The resulting interval is (0.297, 0.383).
Step-by-step explanation:
To construct a 99% confidence interval, we will use the formula:
CI = p-hat ± Z * sqrt((p-hat * (1-p-hat)) / n)
Substituting in the given values: n = 570 and p-hat = 0.34, we can calculate the confidence interval:
CI = 0.34 ± Z * sqrt((0.34 * (1-0.34)) / 570)
To find the value of Z, we need to determine the critical value associated with a 99% confidence level. Looking up the value in a standard normal distribution table, Z ≈ 2.576.
Plugging in this value and completing the calculation, we get:
CI ≈ 0.34 ± 2.576 * sqrt((0.34 * (1-0.34)) / 570)
CI ≈ 0.34 ± 0.043
Therefore, the confidence interval is approximately (0.297, 0.383).