Question

A simple random sample of 500 individuals provides 250 Yes responses. a. What is the point estimate of the proportion of the population that would provide Yes responses (to 3 decimals, if needed)? b. What is your estimate of the standard error of the proportion (to 4 decimals)? c. Compute the 95% confidence interval for the population proportion (to 3 decimals).

Answer 1

The point estimate for confidence interval of proportion is sample proportion which is calculated as:

P n

Where X is the nuumber of individulas who provides yes and n is total random sample.

Now the sample proportion is calculated as:

P X N 250 500 0.5

b) The standard error for population proportion is calculated as:

p(1 - ) EV n

(0.5(1-0.5) 500

= 0.0224

c) The confidence interval is computed as:

P(1 – f), g + ZeV P(1-P) P- #c n n

Where Zc at 95% confidence level is computed using the excel formula for normal distribution which is =NORM.S.INV(0.975), Thus the confidence interval is computed as 1.96.

Now the confidence interval is computed as:

0.5 - 1.96 x 0.5(1 – 0.5) 500 0.5 + 1.96 x 0.5(1 -0.5) 500

- (0.456, 0.544)