Final answer:
To create a 99% confidence interval for the proportion of adults who were victims of a crime, we can use the formula CI = p ± Z * √((p*(1-p))/n). Given that 75 out of 200 adults were victims of a crime, the 99% confidence interval is approximately 0.315 to 0.435.
Step-by-step explanation:
To create a 99% confidence interval for the true proportion of adults who were victims of a crime, we can use the formula:
CI = p ± Z * √((p*(1-p))/n)
Where:
CI is the confidence interval
p is the proportion of the sample who were victims of a crime
Z is the z-value corresponding to the desired confidence level
n is the sample size
Given that 75 out of 200 adults were victims of a crime, the point estimate for the proportion is 75/200 = 0.375. With a 99% confidence level, the corresponding z-value is approximately 2.576.
Plugging these values into the formula, we get:
CI = 0.375 ± 2.576 * √((0.375*(1-0.375))/200)
Simplifying, we find that the 99% confidence interval for the true proportion of adults who were victims of a crime is approximately 0.315 to 0.435.