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90% Confidence Interval Formula:
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A 90% confidence interval (CI) is a range of values that is likely to contain the true population parameter with 90% confidence. It's calculated using the sample mean and standard error, with the formula:
The calculator uses the standard formula for a 90% confidence interval:
Where:
Key Points: The 1.645 multiplier comes from the standard normal distribution, where 90% of values fall within ±1.645 standard deviations from the mean.
Appropriate Uses: This calculator is ideal when you have normally distributed data or large samples (n ≥ 30) where the Central Limit Theorem applies.
Requirements: You need to know the sample mean and standard error. For small samples or non-normal data, consider using t-distribution instead.
Interpretation: If you repeated your study many times, 90% of the calculated confidence intervals would contain the true population mean.
Example: A 90% CI of 45 to 55 means we're 90% confident the true population mean lies between these values.
Q1: Why use 90% instead of 95% confidence?
A: A 90% CI gives a narrower range but less confidence than 95%. It's often used when you want a balance between precision and confidence.
Q2: How is standard error calculated?
A: Standard error is typically calculated as \( SE = \frac{SD}{\sqrt{n}} \), where SD is standard deviation and n is sample size.
Q3: When should I use z-score vs t-score?
A: Use z-score (1.645) for large samples (n ≥ 30) or when population SD is known. Use t-score for small samples with unknown population SD.
Q4: Can I calculate CI for proportions?
A: Yes, the same formula applies for proportions with appropriate standard error calculation.
Q5: What if my data isn't normally distributed?
A: For non-normal data with small samples, consider non-parametric methods or transformations.