How should I construct a confidence interval for the population proportion p with n equals 144 and x equals 82 with a 90 percent confidence level?

The confidence interval will be Pi+-z*sp
z5%= 1.6449
Pi = x/n
Sp = Sqrt(Pi(1-Pi)/n)
Pi ~= 0.5694
Sp = Sqrt(.5694*0.4306/144) ~= 0.0413

Pi - 0.0679 < p < Pi + 0.0679

0.5016 < p < 0.6373

You can do this on your TI-83/84 with 1-PropZInt (Stat->Tests->A)