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.† At a high school, a random sample of n = 66 students (ages 16-19) showed that r = 11 had been victims of a crime. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer (b) Find a 90% confidence interval for the proportion of students in this school (ages 16-19) who have been victims of a crime. (Round your answer to three decimal places.) lower limit upper limit (c) How large a sample size should be used to be 95% sure that the sample proportion p̂ is within a margin of error E = 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 p̂ as a preliminary estimate for p. (Round your answer up to the nearest student.) students
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.† At a high school, a random sample of
(ages 16-19) showed that
had been victims of a crime. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer
(b) Find a 90% confidence interval for the proportion of students in this school (ages 16-19) who have been victims of a crime. (Round your answer to three decimal places.)
| lower limit | |
| upper limit |
(c) How large a sample size should be used to be 95% sure that the sample proportion p̂ is within a margin of error
of the population proportion of all students in this school (ages 16-19) who have been victims of a crime? Hint: Use sample data p̂ as a preliminary estimate for p. (Round your answer up to the nearest student.)
students
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