Question

A 90% confidence interval for a population proportion is given as 0.641 < p < 0.767. Round your answers to 3 decimal places.

(a) Calculate the sample proportion.
p̂ =  

(b) Calculate the margin of error.
E =

Answer 1

SOLUTION:

From given data,

A 90% confidence interval for a population proportion is given as 0.641 < p < 0.767.

given ,

0.641 < p < 0.767

(a) Calculate the sample proportion.(p̂)

This is a symmetric CI , hence sample proportion

p̂ =( 0.641+0.767) / 2

= 1.408 / 2

= 0.704

p̂ = 0.704

(b) Calculate the margin of error.(E)

Margin of error = E = 1/2 * Length of CI

= (0.767-0.641)/ 2

= 0.126/2

= 0.063

E =0.063