Consider estimating the 95% confidence interval for the difference between two population means with a desired margin of error of 5 cm. What would the approximate (i.e., using the 2SE rule of thumb) minimum sample size be for each of the samples if the population standard deviation is 15 cm?

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Quizplus · Accepted Answer

The formula for the margin of error (ME) in estimating the difference between two means is ME = z * sqrt((σ₁²/n₁) + (σ₂²/n₂)), where z is the z-score for the desired confidence level, σ₁ and σ₂ are the population standard deviations, and n₁ and n₂ are the sample sizes. For a 95% confidence interval, z is approximately 1.96. Assuming equal standard deviations (σ₁ = σ₂ = 15 cm) and equal sample sizes (n₁ = n₂ = n), the formula simplifies to ME = 1.96 * sqrt(2 * 15² / n). Setting ME to 5 cm and solving for n gives n ≈ 72.

Consider Estimating the 95% Confidence Interval for the Difference Between