For questions 25 assume that all criteria for constructing t

For questions 2-5, assume that all criteria for constructing the confidence intervals were met.

Question #2:

According to a 2003 National Household Survey on Drug Use and Health, 263 out of 1,546 randomly selected Americans between the ages of 18 and 25 admitted to smoking marijuana during the last month. Construct and interpret a 98% confidence interval for the population proportion.   PLEASE SHOW WORK THANKS

Pl

Solution

p=263/1546= 0.1701164

Given a=0.02, Z(0.01) = 2.33 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.1701164 - 2.33*sqrt(0.1701164*(1-0.1701164)/1546) =0.1478509

So the upper bound is

p + Z*sqrt(p*(1-p)/n) = 0.1701164 + 2.33*sqrt(0.1701164*(1-0.1701164)/1546) =0.1923819

We have 98% confident that the popoulation proportion will be within this interval.