In the 2011 National Crime Victimization Study, the Federal Bureau of Investigation (FBI) found that 16.2% of Americans age 12 or older had been victims of crime during a 1-year period. This result was based on a sample of 143,120 persons.
a. Estimate the percentage of U.S. adults who were victims at the 90% confidence level. State in words the meaning of the result.
b. Estimate the percentage of victims at the 99% confidence level.
c. Imagine that the FBI cuts the sample size in half but finds the same value of 16.2% for the percentage of victims in the second sample. By how much would the 90% confidence interval increase? By how much would the 99% confidence interval increase?
d. Considering your answers to (a), (b), and (c), can you suggest why national surveys, such as those by Gallup, Roper, or The New York Times, typically take samples of size 1,000 to 1,500?