📊 PLS 120: Week 6 - T-Tests & Confidence Intervals Lab

🎯 Week 6 Key Concepts

T vs Z Distribution

Use t when σ unknown

T-distribution has heavier tails, especially for small samples (n < 30)

T-Based CI

x̄ ± t(s/√n)

More conservative intervals when population σ is unknown

One-Sample T-Test

t = (x̄-μ₀)/(s/√n)

Test if sample mean differs significantly from hypothesized value

Degrees of Freedom

df = n - 1

Smaller df = wider distribution, larger critical values

📈 T vs Z Distribution Comparison

🔍 Interactive Distribution Comparison

⚙️ Distribution Settings

Sample Size (n)

n = 15 (df = 14)

Confidence Level

📊 Critical Values

Adjust settings to see the comparison!

📈 T vs Z Distribution Curves

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Distribution comparison will appear here

🧮 One-Sample T-Test Calculator

🌾 Wheat Yield T-Test Example

📊 Sample Data

Sample Mean (x̄) - bushels/acre

Sample Standard Deviation (s)

Sample Size (n)

Hypothesized Mean (μ₀)

Significance Level (α)

📈 T-Test Results

Enter sample data to see t-test results!

📊 T-Test Visualization

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T-test visualization will appear here

📏 Confidence Intervals: T vs Z

🔬 CI Comparison Tool

⚙️ Sample Parameters

Sample Mean

Sample Standard Deviation

Sample Size

Confidence Level

📊 Interval Comparison

Adjust parameters to see CI comparison!

📈 Confidence Intervals Visualization

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Confidence intervals comparison will appear here

🌾 Agricultural Treatment Comparison

🧪 Control vs Fertilizer Treatment

🌱 Control Group

Sample Size

Mean Yield (bu/acre)

Standard Deviation

🌿 Fertilizer Treatment

Sample Size

Mean Yield (bu/acre)

Standard Deviation

📊 Treatment Analysis

Enter treatment data to see the analysis!

📈 Treatment Comparison Visualization

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Treatment comparison will appear here

🎯 Practice Quiz

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🎓 Key Takeaways

📊

When to Use T-Distribution

• Population σ is unknown
• Using sample standard deviation (s)
• Small to moderate sample sizes
• More conservative than z-distribution

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T-Test Interpretation

• |t| > t-critical → Reject H₀
• p-value < α → Significant result
• Consider practical significance
• Check assumptions (normality)

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Agricultural Applications

• Test treatment effectiveness
• Estimate population parameters
• Compare confidence intervals
• Make data-driven decisions