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

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

$z\sqrt{\dfrac{p(1-p)}{n}}\\\\=1.645\times \sqrt{\dfrac{0.132\times 0.868}{1152}}}\\\\=0.0164$

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.