Question

In a study of crime, the FBI found that 13.2% of all Americans had been victims of crime during a 1-year period. This result was based on a sample of 1,105. Estimate the percentage of U.S. adults who were victims at the 90% confidence level. What is the lower bound of the confidence interval?

Answer 1

The confidence interval for percentage of U.S. adults who were victims of crime at the 90% confidence level is (0.114, 0.15). The lower bound of the confidence interval is 0.114.

Step-by-step explanation:

To estimate the percentage of U.S. adults who were victims of crime at the 90% confidence level, we can use the formula for a confidence interval:

`CI = p +/- Z * \sqrt{((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. In this case, p = 0.132, Z = 1.645 (corresponding to a 90% confidence level), and n = 1105. Plugging in these values, we can calculate the confidence interval as:

`CI = 0.132 +/- 1.645 * \sqrt((0.132 * (1-0.132)) / 1105)`

Simplifying the expression gives us:

CI = 0.132 ± 0.018

Therefore, the confidence interval for the percentage of U.S. adults who were victims of crime at the 90% confidence level is (0.114, 0.15). The lower bound of the confidence interval is 0.114.

Answer 2

Answer: The lower bound of confidence interval would be 0.116.

Step-by-step explanation:

Since we have given that

p = 13.2%= 0.132

n = 1105

At 90% confidence,

z = 1.645

So, Margin of error would be

`z\sqrt{(p(1-p))/(n)}\\\\=1.645* \sqrt{(0.132* 0.868)/(1152)}}\\\\=0.0164`

So, the lower bound of the confidence interval would be

`p-\text{margin of error}\\\\=0.132-0.0164\\\\=0.116`

Hence, the lower bound of confidence interval would be 0.116.