You wish to estimate with $90\%$ confidence the population proportion of people in Gen-Z that use social media. If you want your estimate to be accurate within $4\%$ of the population proportion, what is the minimum sample size needed? 

• A. 422
• B. 423
• C. 405
• D. 406

Answer: (B)

Verified step by step guidance

1. Identify the confidence level and margin of error: The confidence level is 90%, and the margin of error is 4% (0.04).
2. Determine the critical value (z-score) for a 90% confidence level. This can be found using a standard normal distribution table or calculator. The z-score for 90% confidence is approximately 1.645.
3. Use the formula for sample size estimation for a proportion: n = (z^2 * p * (1-p)) / E^2, where n is the sample size, z is the z-score, p is the estimated population proportion, and E is the margin of error.
4. Assume the most conservative estimate for the population proportion, p = 0.5, to ensure the maximum sample size. This is because the product p*(1-p) is maximized when p = 0.5.
5. Substitute the values into the formula: n = (1.645^2 * 0.5 * 0.5) / 0.04^2. Calculate the result to find the minimum sample size needed.