Question

In its Audit of Computerized Criminal History, the Florida Department of Law Enforcement (FDLE) periodically reviews the accuracy and completeness of its criminal history database. The database contains thousands of records. The FBI/Bureau of Justice Quality Standards require that at least 95% of all records in the state’s database be complete and accurate. The audit uses a simple random sample to determine whether the state has met the standard. In a recent FDLE audit, the auditor found that only 555 records of the 605 records sampled were perfectly complete and accurate; the others were either incomplete or contained at least one error (source: fdle. state.fl.us/ publications/). Is this sample evidence sufficient to reject, at the 5% significance level, a null hypothesis that the population of Florida criminal records meets FBI/Bureau of Justice Quality Standards? Explain.

Answer 1

Given that

sample size =n=605

No.of records perfectly complete and accurate=x=555

we need to test that the population of Florida criminal records meets FBI/Bureau of Justice Quality Standards or not so for meeting the standards there should at least 92% records that are complete and accurate so we need to test that proportion is at least 0.92 or not so

H0: P>0.92 H1:P<0.92

now sample proportion is given by

Now test statistics is given by

Since test is left tailed so

P-Value=P(Z<-0.2448)=0.4033

Since P Value is more than level of significance hence we failed to reject H0 hence we do not have sufficient statistical evidence to conclude that proportion is less than 92% Hence

at the 5% significance level we failed to reject a null hypothesis that the population of Florida criminal records meets FBI/Bureau of Justice Quality Standards