Question

A random sample of 725 shoppers showed that 621 remained loyal to their favorite brands during the last year. Construct a 99% confidence interval for the proportion of shoppers that remain loyal to their favorite brands.

What is the Point Estimate, Margin of Error, Lower Limit, Upper Limit, and how do you get these answers?

Answer 1

Solution :

Given that,

n = 725

x = 621

Point estimate = = x / n = 621 / 725 = 0.857

1 - = 1 - 0.857 = 0.143

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.857 * 0.143) / 725)

= 0.034

Margin of error = 0.034

A 99% confidence interval for population proportion p is ,

- E < P < + E

0.857 - 0.034 < p < 0.857 + 0.034

0.823 < p < 0.891

(0.823 , 0.891)

Lower limit = 0.823

Upper limit = 0.891