Question

The article "Should Canada Allow Direct-to-Consumer Advertising of Prescription Drugs?"† calls for the legalization of advertising of prescription drugs in Canada. Suppose you wanted to conduct a survey to estimate the proportion of Canadians who would allow this type of advertising. How large of a random sample would be required to estimate this proportion with a margin of error of 0.02?

Answer 1

To estimate the proportion of Canadians who would allow the advertising of prescription drugs with a 0.02 margin of error, a random sample of 2,401 Canadians is required using the sample size estimation formula, assuming a 95% confidence level.

Step-by-step explanation:

To estimate the proportion of Canadians who would allow direct-to-consumer advertising of prescription drugs with a margin of error of 0.02, it's necessary to calculate the required sample size using the formula for sample size estimation:

n = (Z^2 * p * (1-p)) / E^2

Where:

• n = sample size
• Z = Z value (the number of standard deviations from the mean)
• p = estimated proportion (since no proportion is given, use 0.5 for maximum variability)
• E = margin of error

Assuming a 95% confidence level (commonly used in practice), the Z value is 1.96. Plugging in the values:

n = (1.96^2 * 0.5 * (1-0.5)) / 0.02^2

Calculating this gives:

n = (3.8416 * 0.25) / 0.0004
n = 0.9604 / 0.0004
n = 2401

Therefore, a random sample of 2,401 Canadians would be required to estimate the proportion with a margin of error of 0.02.