Question

A simple random sample of 700 individuals provides 200 Yes responses. a. What is the point estimate of the proportion of the population that would provide Yes responses (to 2 decimals)? 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 4 decimals).

Answer 1

Answer and Explanation:

A. The point estimate of individuals that would provide yes responses is the sample proportion. The sample proportion is calculated by dividing number of yes responses by sample size:

p = x/n = 200/700= 0.2857

B. The standard error of the population is the square root of the product of the point estimate and it's complement divided by the sample size given by

√p(1-p)/n

=√0.2857(1-0.2857)/700= 0.0170

C. For confidence level 95%, z score is calculated 1-0.95= 0.05/2= 0.025

Z score checked under the table = 1.96

Boundaries=

P-1.96 *standard error and p+1.96 *standard error

= 0.2857-1.96*0.0170= -0.25238

=0.2857+1.96*0.0170= 0.31902

Note : BODMAS demands we multiply first in the above calculation before subtraction or addition.