Testing and Estimating a Proportion p Although older Americans are most afraid of crime, it is young people who are more likely to be the actual victims of crime. It seems that older people are more cautious about the people with whom they associate. A national survey showed that 10% of all people ages 16–19 have been victims of crime (Reference: Bureau of Justice Statistics). At Jefferson High School, a random sample of n 5 68 students (ages 16–19) showed that r 5 10 had been victims of a crime.

(a) Do these data indicate that the population proportion of students in this school (ages 16–19) who have been victims of a crime is different (either way) from the national rate for this age group? Use a 5 0.05.
Do you think the conditions np 5 and nq 5 are satisfi ed in this setting? Why is this important?

(b) Find a 90% confi dence interval for the proportion of students in this school (ages 16–19) who have been victims of a crime.

(c) How large a sample size should be used to be 95%
sure that the sample proportion pˆ is within a margin of error E 5 0.05 of the population proportion of all students in this school (ages 16–19) who have been victims of a crime? Hint: Use sample data pˆ as a preliminary estimate for p.