Question

3) Television viewers often express doubts about the validity of certain commercials. In an attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 89% confident that their estimate will fall within 1% of the true population proportion?

Answer 1

Solution,

Given that,

= 0.40

1 - = 1 - 0.40 = 0.60

margin of error = E = 0.01

At 89% confidence level

= 1 - 89%

= 1 - 0.89 =0.11

/2 = 0.055

Z/2 = Z0.055  = 1.60

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.60 / 0.01 )2 * 0.40 * 0.60

= 6144

sample size = n = 6144