šŸ“š Essential Formulas

Confidence Interval

xĢ„ Ā± z(s/āˆšn)

Standard Error

SE = s/āˆšn

Sample Size

n = zĀ²p(1-p)/dĀ²

Z-Score

z = (x-Ī¼)/Ļƒ

šŸŽÆ Understanding Confidence Intervals

šŸ“Š Your Sample's Confidence Interval

šŸŽ² Take a Sample

šŸ“ˆ Your Results

Take a sample to see your confidence interval!

šŸ“ Confidence Interval Visualization

šŸ“Š

Your confidence interval will appear here

šŸ”¬ What Does "95% Confidence" Really Mean?

āš™ļø Simulation Settings

šŸ“Š Results

Run simulation to see the results!

šŸ“ˆ 20 Different Studies (Horizontal View)

šŸ”¬

Simulation results will appear here

šŸ“ How Sample Size Affects Precision

Small Sample (n=25)

Wide Interval Ā±8.2

Medium Sample (n=50)

Medium Interval Ā±5.8

Large Sample (n=100)

Narrow Interval Ā±4.1

šŸ“Š Sample Size Comparison

Click a sample size button above to see the comparison!
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What 95% Confidence Means

If we repeated our study 100 times, about 95 of the confidence intervals would contain the true population parameter (Ī¼).

šŸ“

Interval Width

Larger samples create narrower intervals (more precise). Higher confidence levels create wider intervals (more certain).

šŸŽÆ

Correct Interpretation

Your specific interval either contains Ī¼ or it doesn't - there's no probability. The confidence is about the method, not your specific interval!

šŸ“ Interactive Z-Score Calculator

šŸŽÆ Understanding Z-Scores

šŸ“Š Enter Your Data

šŸ“ˆ Z-Score Results

Enter values to see z-score calculation!

šŸ“Š Normal Distribution Visualization

Z-score visualization will appear here

šŸŒ¾ Real Agricultural Examples

šŸŒ± Crop Yield Study

62.3 Ā± 3.8 bu/acre
95% Confidence Interval

Sample of 50 fields shows average corn yield between 58.5 and 66.1 bushels per acre.

Interpretation:
We're 95% confident the true average yield for this region is between 58.5 and 66.1 bu/acre.

šŸ› Pest Infestation Rate

12.4% Ā± 4.2%
90% Confidence Interval

Survey of 80 fields shows pest damage rate between 8.2% and 16.6%.

Decision:
Since the entire interval is above 8%, recommend preventive treatment for the region.

šŸŒ§ļø Rainfall Prediction

28.7 Ā± 6.1 inches
95% Confidence Interval

Historical data suggests annual rainfall between 22.6 and 34.8 inches.

Planning:
Design irrigation systems to handle drought conditions (22.6 inches minimum).

šŸŽÆ Practice Quiz

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