If n=530 and p' (p-prime) = 0.78, construct a 90% confidence interval. Give your answers to three decimals.

Answer 1

Hi Salma,

p’ and p-hat are equivalent, so formula for this confidence interval is:

CI=p-hat +/- z*SE

Let’s break this down.

p-hat=p’=sample proportion

z*=z-critical value=1.645 (90% is common confidence level, so this is worth memorizing)

SE=standard error

Now, we have:

p’=0.78

z*=1.645

Standard error (SE) has its own formula. It is:

SE=sqrt[(p’(1-p’))/n]

p’=sample proportion

n=sample size

For this problem:

p’=0.78

1-p’=0.22

n=530

So:

SE=sqrt[(0.78*0.22)/530]

SE=0.018

Now, we can compute our confidence interval:

CI=p’ +/- z*SE

p’=0.78

z*=1.645

SE=0.018

CI=0.78 +/- (1.645*0.018)

CI=(0.750, 0.810)

I hope this helps.