As you learned on page 544, recent research by R. Brame et al. indicates that almost a third of Americans have been arrested by age 23, and this figure excludes arrests for minor traffic violations. Now that you have studied inferences for proportions, we ask you to conduct statistical analyses based on the results obtained by the researchers. A random sample of 6157 Americans revealed that 1858 had been arrested by the time they were 23 years old.
a. Obtain and interpret a point estimate for the percentage of Americans who have been arrested by age 23.
b. Assuming a simple random sample, determine and interpret a 95% confidence interval for the percentage of Americans who have been arrested by age 23.
c. At the 1% significance level, do the data provide sufficient evidence to conclude that the percentage of Americans who have been arrested by age 23 is less than a third?
d. At the 1% significance level, do the data provide sufficient evidence to conclude that the (current) percentage of Americans who have been arrested by age 23 exceeds the 1965 percentage of 22%?