Final answer:
To calculate the 95% confidence interval, you can use the formula CI = p ± Z * sqrt((p * (1 - p)) / n), where p is the sample proportion, Z is the critical value, and n is the sample size. Applying this formula to the given data, the 95% confidence interval for the percentage of millennials who believe their generation has a distinctive identity is 57% to 65%.
Step-by-step explanation:
To calculate the 95% confidence interval to estimate the percentage of millennials who believe that their generation has a distinctive identity, we can use the formula:
CI = p ± Z * sqrt((p * (1 - p)) / n)
where CI is the confidence interval, p is the sample proportion, Z is the critical value from the standard normal distribution, and n is the sample size.
iven that the sample proportion is 61%, the sample size is 527, and the critical value for a 95% confidence level is approximately 1.96, we can substitute these values into the formula:
CI = 0.61 ± 1.96 * sqrt((0.61 * (1 - 0.61)) / 527)
Calculating the lower and upper bounds of the confidence interval:
Lower bound = 0.61 - 1.96 * sqrt((0.61 * 0.39) / 527) ≈ 0.57
Upper bound = 0.61 + 1.96 * sqrt((0.61 * 0.39) / 527) ≈ 0.65
Therefore, the 95% confidence interval to estimate the percentage of millennials who believe that their generation has a distinctive identity is 57% to 65%.