Question

Saatchi and Saatchi, a London-based advertising agency, shows two television commercials to a sample of 60 people. Seventy percent of these individuals prefer the first commercial over the second. Construct a 95 % confidence interval for the proportion of all members of the relevant population who feel that way.

Answer 1

Solution :

Given that,

n = 60

Point estimate = sample proportion = = 70% = 0.70

1 - = 1 - 0.70 = 0.30

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.70 * 0.30) / 60)

= 0.116

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.70 - 0.116 < p < 0.70 + 0.116

0.584 < p < 0.816

(0.584 , 0.816)