Confidence Interval Calculator

Steps for Calculation

1. Input Values:
   • Sample Mean: Enter the mean of the sample data (e.g., 50).
   • Sample Size: Enter the number of observations in the sample (e.g., 100).
   • Standard Deviation: Enter the standard deviation of the sample (e.g., 10).
   • Confidence Level: Enter the confidence level as a percentage (e.g., 95 for 95%).
2. Calculate Confidence Interval:
   • Click the Calculate Confidence Interval button to compute the confidence interval.
3. View Result:
   • The confidence interval will be displayed below the button.

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Detailed Description

• Confidence Interval:
  • A confidence interval is a range of values that is likely to contain the population mean with a specified level of confidence.
  • Formula: Confidence Interval=Sample Mean±(Z⋅Standard Error)Confidence Interval=Sample Mean±(Z⋅Standard Error).
  • Where:
    • ZZ = Z-score (based on the confidence level),
    • Standard Error=Standard DeviationSample SizeStandard Error=Sample Size​Standard Deviation​.
• Z-Score:
  • The Z-score is determined by the confidence level. Common Z-scores are:
    • 80% confidence level: 1.28
    • 85% confidence level: 1.44
    • 90% confidence level: 1.645
    • 95% confidence level: 1.96
    • 99% confidence level: 2.576
• Example Calculation:
  • For a sample mean of 50, sample size of 100, standard deviation of 10, and confidence level of 95%:
    • Z-score = 1.96,
    • Standard Error = 10100=1100​10​=1,
    • Margin of Error = 1.96×1=1.961.96×1=1.96,
    • Confidence Interval = (50−1.96,50+1.96)=(48.04,51.96)(50−1.96,50+1.96)=(48.04,51.96).