142 out of 507 people were right. Calculate a 95% confidence interval for the proportion of the entire population that could be right. I did some of the work …Please help.

Question

I am getting .0199 SD =sqt(.28(1-.28)/506 = .0119 so .28 +/- .0119
so I could say that with 95% confidence, between 26.81% and 29.19% of the entire population could be right?

Answer 1

YES. IF YOUR PROFESSOR SAID THAT YOUR ANSWER SHOULD BE IN PERCENT.

P = 142/507 = 0.28

SD = SQRT( .28*.72/507)

SQRT(0.2016/507) = 0.0199

1-a = .95

a =0.05

za/2 = z0.025 = 1.96

Z = 1.96

p -+ za/2 * SD/sqrt(n)

0.28-+1.96*0.0199

0.28-+ 0.039

( 0.241, 0.319)

IF YOUR PROFESSOR SAID THAT YOUR ANSWER SHOULD BE IN PERCENT.

95% confidence interval is between 24.1% and 31.9%.