Question

An advertising executive thinks that the proportion of consumers who have seen his company advertisement in newspaper is around 0.65. The executive want to estimate the customer proportion to within ± 0.05 and have a 98% confidence in the estimate. How large a sample should be taken?

Answer 1

To determine the sample size required to estimate the proportion of consumers who have seen the company's advertisement in the newspaper, we can use the formula for sample size calculation for proportions. The formula is as follows:

n = (Z^2 * p * q) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, 98% confidence corresponds to a Z-score of approximately 2.33)

p = estimated proportion (0.65)

q = 1 - p (the complement of the estimated proportion)

E = maximum error tolerance (+/- 0.05)

Let's plug in the values and calculate the sample size:

n = (2.33^2 * 0.65 * 0.35) / (0.05^2)

n = 339.28

Rounding up to the nearest whole number, the required sample size is 340.