Final answer:
To calculate the 95% confidence interval for the proportion of Kansas teachers thinking of retiring in the next five years, we can use the formula CI = p ± Z * √(p(1-p) / n), where p is the sample proportion, Z is the Z-score, and n is the sample size. The confidence interval is approximately (0.2326, 0.3452), or 23.26% to 34.52%.
Step-by-step explanation:
To calculate the 95% confidence interval for the proportion of Kansas teachers who were thinking of retiring in the next five years, we can use the formula:
CI = p ± Z * √(p(1-p) / n)
where CI is the confidence interval, p is the sample proportion, Z is the Z-score corresponding to the desired confidence level, and n is the sample size.
From the given information, we have p = 52/180 = 0.2889, n = 180, and the Z-score for a 95% confidence level is approximately 1.96 (obtained from a standard normal distribution table).
Plugging these values into the formula, we get:
CI = 0.2889 ± 1.96 * √(0.2889(1-0.2889) / 180)
Calculating the formula, the confidence interval for the proportion of Kansas teachers thinking of retiring in the next five years is approximately (0.2326, 0.3452), or 23.26% to 34.52%.