9. (Crime) In the U.S., there are two sources of national statistics on crime ra

Question

9. (Crime) In the U.S., there are two sources of national statistics on crime rates: (i) the FBI's Uniform Crime Reporting Program, which publishes summaries on all crimes reported to police agencies in jurisdictions covering virtually 100% of the US.(ii) the National Crime Survey (NCS), which is based on in terviews with a nationwide probability sample of households. In 1992, 4.9% of the households in the NCS sample told the interviewers thev had experi- enced a burglary within the past 12 months. The same year, the FBI reported a burglary rate of 32 per 1,000 households, or 3.2%, for the US. as a whole. If the FBI's 3.2% figure is the true burglary rate for the population of US households in 1992, what is the probability that the National Crime Survey would obtain a result of 4.9% or more? You may assume that the NCS is based on a simple random sample of 50,000 households out of a population of 100 million households. What do vou conclude?

Explanation / Answer

QUestion 9

(a) Here true burglery rate = 3.2% = 0.032

sample size n = 50,000

standard error of proportion = sqrt [0.032 * (1 - 0.032)/50000] = 7.87 * 10-4

so here we have to find the probability that

Pr(p > 0.049 ; 0.032 ; 7.87 * 10-4)

Z = (0.049 - 0.032)/ (7.87 * 10-4)

Z = 21.60

so here for the given Z value

Pr(p > 0.049 ; 0.032 ; 7.87 * 10-4) = Pr(Z > 21.60) = 0

so we conclude that the NCS sample survey doesn't agree with FBI reported burglery rate..

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