Final answer:
To determine the required sample size for a 95% confidence interval with a width of 0.1033 for the proportions of residents of two-story houses who own their house, use the formula Sample Size = (Z^2 * p * (1-p)) / E^2, where Z is the z-score corresponding to the desired confidence level, p is the worst-case proportion, and E is the desired width of the confidence interval.
Step-by-step explanation:
To determine the required sample size for a 95% confidence interval with a width of 0.1033, we need to find the minimum number needed to estimate the population proportion of residents who own two-story houses. Since nothing is known about the population proportion, we can use the worst-case scenario where the proportion is 0.5.
To calculate the required sample size, we can use the formula:
Sample Size = (Z^2 * p * (1-p)) / E^2
Z is the z-score corresponding to the desired confidence level (in this case, 95% confidence corresponds to a z-score of 1.96). p is the worst-case proportion (0.5), and E is the desired width of the confidence interval (0.1033).
Plugging in the values, we get:
Sample Size = (1.96^2 * 0.5 * (1-0.5)) / 0.1033^2
Sample Size = 384.122
Rounding up to the nearest whole number, the required sample size is 385.