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 LOWER LIMIT of the confidence interval of the percentage of victims at the 99% confidence level.

Please round to the nearest whole number.

Answer 1

11%

Explanation:

The margin of error is the standard error times the critical value.

For a proportion, the standard error is:

σ = √(pq / n)

σ = √(0.132 × 0.868 / 1105)

σ = 0.0102

Since n is large, we can approximate the critical value using a normal distribution. For 99% confidence, the critical value is 2.576.

The margin of error is:

ME = 0.0102 × 2.576

ME = 0.026

The confidence interval is 0.132 ± 0.026. So the lower limit is 0.106, or 10.6%. Rounded to the nearest whole number, that's 11%.