Phần hướng dẫn bên dưới chưa có bằng tiếng Việt nên được hiển thị bằng tiếng Anh. Bản thân máy tính đã được dịch đầy đủ.
Cách sử dụng máy tính này
- Choose an interval for a mean or for a proportion.
- For a mean, enter the sample mean, standard deviation and sample size, and choose whether the SD is from the sample (t) or known for the population (z).
- For a proportion, enter the sample size and number of successes.
- Choose the confidence level.
Công thức
A confidence interval is the estimate plus or minus a margin of error. When the population SD is unknown (the usual case), the critical value comes from Student's t distribution with n − 1 degrees of freedom.
Mean: x̄ ± t* × s / √n
Mean (σ known): x̄ ± z* × σ / √n
Proportion (Wilson): (p̂ + z²/2n ± z√(p̂(1−p̂)/n + z²/4n²)) / (1 + z²/n)
Example
- x̄ = 50, s = 8, n = 40, 95% confidence: t*(39) ≈ 2.0227.
- SE = 8 / √40 ≈ 1.2649; margin ≈ 2.5585.
- 95% CI ≈ 47.44 to 52.56.
Câu hỏi thường gặp
What does 95% confidence mean?
If you repeated the sampling many times, about 95% of the intervals built this way would contain the true value. It does not mean there is a 95% probability that this particular interval contains it.
When should I use t instead of z?
Use t whenever the standard deviation is estimated from your sample. For large samples (n > 100) t and z are nearly identical.
How can I make the interval narrower?
Increase the sample size (the margin shrinks with √n) or accept a lower confidence level.