Question

An advertising firm plans to have a sample of individuals view a commercial on a ‘‘sunscreen pill” that one can swallow to provide mild SPF protection throughout the day. After viewing the commercial, each individual will be asked if he/she would consider buying the product. How many individuals should the firm sample to estimate the proportion who would consider buying the product to within a plus-or-minus 4 % margin of error with 90% confidence?

Round your answer up to the nearest integer.

sample size =

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.04

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.1 is 1.645.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(1.645/0.04)^2
n = 422.82

Therefore, the sample size needed to satisfy the condition n >= 422.82 and it must be an integer number, we conclude that the minimum required sample size is n = 423

Ans : Sample size, n = 423