Question

A simple random sample of 700 individuals provides 300 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

a. What is the point estimate of the proportion of the population that would provide Yes response

p^=x/n=300/700= 0.4285714=0.43

0.43

b. What is your estimate of the standard error of the proportion (to 4 decimals)?

SE=sqrt(p^*(1-p^)/n

= sqrt(0.4285714*(1-0.4285714)/700)

= 0.01870439

= 0.0187

standard error= 0.0187

c. Compute the 95% confidence interval for the population proportion (to 4 decimals).

95% confidence interval for p is

p^-z*sqrt(p^*(1-p^)/n,p^+z*sqrt(p^*(1-p^)/n

z crit for 95%=1.96

0.4285714-1.96*sqrt(0.4285714*(1-0.4285714)/700),0.4285714+1.96*sqrt(0.4285714*(1-0.4285714)/700)

0.3919108,0.465232

0.3919,0.4652

(0.3919,0.4652)