Question

a) Construct a 97% confidence interval attempting to capture the population proportion of people who wear seat belts. Make sure you show the final CI in the only acceptable form for this class. Show your PE, TS, SE, and ME in addition to your final interval.  

b) Can you say that more than 75% of the population complies? Why?

c) Can you say that more than 80% of the population complies? Why?

d) Can you say that less than 85% of the population complies? Why?

Answer 1

confidence interval for proportion =

(p^ +- z *sqrt(p^(1-p^)/n))

z = 2.17 for 97% level

PE is point estimate = p^ = X/n

SE = standard error =sqrt(p^(1-p^)/n))

ME = margin of error = z *sqrt(p^(1-p^)/n))

b)

if lower bound of CI (confidence interval) is more than 0.75, then we can say more than 75% of the population complies

c)

if lower bound of CI (confidence interval) is more than 0.8, then we can say more than 80% of the population complies

d)

if upper bound of CI (confidence interval) is less than 0.85, then we can say more than 85% of the population complies