Question

A simple random sample of 400 individuals provides 128 Yes responses.

(a)

What is the point estimate of the proportion of the population that would provide Yes responses?

(b)

What is your estimate of the standard error of the proportion,

σp?

(Round your answer to four decimal places.)

(c)

Compute the 95% confidence interval for the population proportion. (Round your answers to four decimal places.)

Answer 1

a)

Sample proportion = 128 / 400 = 0.32

point estimate of proportion = 0.32

b)

Standard error = sqrt ( ( 1 - ) / n)

= sqrt( 0.32 * 0.68 / 400)

= 0.0233

c)

95% confidence interval is

- Z * SE < p < + Z * SE

0.32 - 1.96 * 0.0233 < p < 0.32 + 1.96 * 0.0233

0.2743 < p < 0.3657

95% CI is ( 0.2743 , 0.3657 )