construct a 95% confidence interval.

Question

If n = 200 and p^ (p-hat) = 0.8, construct a 95% confidence interval.

Give your answers to three decimal

Answer 1

Hi Kaitlyn,

Finally an actual confidence interval for proportion.

Formula is CI=p +/- z*sqrt(p(1-p)/n))

You will sometimes see p denoted p-hat just because it is an estimate.

Now, let's make sure we have a large enough sample to assume normality:

np>=10

n(1-p)>=10

n=200

p=0.8

np=160

1-p=0.2

n(1-p)=40

We're good to go. Setting up values for our confidence interval:

p=0.80

z*=1.96, z-score for 95% confidence

n=200

CI= 0.8 +/- 1.96*sqrt[((0.8*0.2)/200)]

CI=0.8 +/- 0.055

CI=(0.745, 0.855)

In a test situation, I hope you get a formulas sheet. These can be tough to remember.