Confidence Interval Calculator
Calculate the confidence interval for a population mean using sample data.
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Table of Contents
What is a Confidence Interval?
A confidence interval is a range of values that is likely to contain the true population parameter with a specified level of confidence. It provides a way to quantify the uncertainty in our estimates.
- Confidence intervals provide a range of plausible values for the population parameter
- The confidence level (e.g., 95%) indicates how often the interval will contain the true parameter
- Wider intervals indicate more uncertainty in the estimate
- Larger sample sizes generally lead to narrower intervals
How to Calculate Confidence Intervals
To calculate a confidence interval for a population mean:
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1Calculate the sample mean
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2Determine the standard deviation
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3Choose the confidence level
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4Calculate the margin of error
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5Construct the interval
Interpreting Confidence Intervals
Understanding what confidence intervals tell us:
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1Confidence Level:
The percentage of intervals that would contain the true parameter if we repeated the sampling process many times.
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2Margin of Error:
Half the width of the interval, representing the maximum likely difference between the sample mean and population mean.
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3Precision:
Narrower intervals indicate more precise estimates of the population parameter.
Practical Examples
Example 1 Student Test Scores
A sample of 50 students has a mean score of 75 with a standard deviation of 10.
95% CI: [72.23, 77.77]
We are 95% confident that the true mean score of all students falls between 72.23 and 77.77.
Example 2 Product Weight
A sample of 100 products has a mean weight of 500g with a standard deviation of 20g.
99% CI: [494.85, 505.15]
We are 99% confident that the true mean weight of all products falls between 494.85g and 505.15g.
Example 3 Customer Satisfaction
A sample of 200 customers has a mean satisfaction score of 4.2 with a standard deviation of 0.8.
90% CI: [4.11, 4.29]
We are 90% confident that the true mean satisfaction score of all customers falls between 4.11 and 4.29.