Welcome to Week 5! This week, we explore sampling distributions and statistical estimation - critical skills for designing agricultural studies and interpreting research results. Learn to calculate sample sizes, construct confidence intervals, and understand estimation precision!

🎯 What You'll Learn This Week

🎲 Reproducible Research - Use set.seed() for consistent random sampling

📏 Z-Score Standardization - Convert data to standard normal distribution

📊 Normal Distribution Functions - Master pnorm(), qnorm(), and rnorm()

🎯 Confidence Intervals - Estimate population parameters with uncertainty

📐 Sample Size Calculations - Determine required sample sizes for studies

📈 Margin of Error - Understand precision trade-offs in estimation

🚀 Getting Started: Step-by-Step Guide

Step 1: Launch Week 5 Binder Environment 🌐

Click the "Launch Week 5" button above to start your R environment. This will take 2-5 minutes to load with all necessary packages for sampling and estimation.

Step 2: Navigate to Class Activity 📚

Once Binder loads, you'll see the Jupyter Notebook interface. In the left panel, you'll see:

assignment/ - Assignment 5 on sample size calculations
class_activity/ - Week 5 lab tutorial
Various files (README.md, runtime.txt, etc.)

Click on the class_activity folder to access this week's content.

Step 3: Open the Week 5 Lab Notebook 📖

Inside the class_activity folder, double-click on Week5_Sampling_Estimation.ipynb to open the interactive lab notebook.

Step 4: Explore Sampling Concepts 📊

This week we'll work with sampling distributions and estimation! The notebook will guide you through:

Understanding reproducible research with set.seed()
Z-score standardization and normal distributions
Constructing confidence intervals for means and proportions
Calculating required sample sizes for different precision levels
Understanding margin of error and confidence level trade-offs

🎯 Interactive Learning Tools

Practice with Sampling and Estimation Tools

Use these interactive tools to understand sampling concepts before working with R code:

💡 Tip: Use these tools to visualize sampling distributions and confidence intervals before applying them in your R notebook!

🧮 Key R Functions This Week

Sample Size and Confidence Intervals

            qnorm(0.975)                           # Z-value for 95% confidence

            ceiling(n)                             # Round up sample size

            mean(data) + c(-1,1) * margin_error    # Confidence interval

            sqrt(p * (1-p) / n)                    # Standard error for proportions

            z^2 * p * (1-p) / d^2                  # Sample size formula

Normal Distribution Functions

            pnorm(x, mean = 0, sd = 1)             # Calculate probabilities

            qnorm(p, mean = 0, sd = 1)             # Find critical values

            rnorm(n, mean = 0, sd = 1)             # Generate random normal data

            scale(data)                            # Standardize data (z-scores)

Reproducible Research

            set.seed(123)                          # Set random seed

            sample(population, n, replace=FALSE)   # Random sampling

            replicate(1000, experiment)            # Repeat simulations

            mean(replicated_results)               # Average over simulations

📝 Assignment 5: Sample Size Calculations

Step 1: Access Assignment Folder 📋

From the main directory, click on the assignment folder to access Assignment 5.

Step 2: Open Assignment 5 Notebook 📄

Double-click on Assignment5.ipynb to open your assignment on sample size calculations.

Assignment Overview (20 points total)

📐

Question 1: Basic Sample Size Calculation (6 points)

Calculate sample size for 95% confidence and 5% margin of error

📊

Question 2: Effect of Prevalence Rate (5 points)

Analyze how prevalence affects required sample size

📏

Question 3: Effect of Margin of Error (5 points)

Understand precision trade-offs in sample size planning

🎯

Question 4: Effect of Confidence Level (4 points)

Compare sample sizes for different confidence levels

Step 3: Calculate Sample Sizes for Health Studies 🏥

The assignment focuses on sample size determination for public health research:

Diabetes Prevalence Study - Calculate required sample sizes for disease estimation
Confidence Level Effects - Compare 90%, 95%, and 99% confidence requirements
Precision Trade-offs - Understand how margin of error affects sample size

Learn to make informed decisions about study design and resource allocation!

🌾 Why This Matters in Agriculture

🌱 Seed Germination Studies - Estimate germination rates with confidence intervals

🌾 Crop Yield Estimation - Sample fields to predict total harvest

🐛 Pest Occurrence Surveys - Calculate sample sizes for pest monitoring

🔬 Quality Control Testing - Design sampling plans for product standards

💰 Agricultural Insurance - Quantify risks using statistical estimation

Sampling Skills Help You:

Design cost-effective studies with appropriate sample sizes
Estimate population parameters with known precision
Make informed decisions about resource allocation
Understand uncertainty in agricultural measurements
Communicate results with confidence intervals

💾 Saving Your Work

⚠️ Important: Binder environments are temporary! Always save your work locally.

Download Your Notebook 📥

When you're done working, save your progress:

Save your notebook: File → Save
Download .ipynb file: File → Download
Export HTML/PDF: File → Save and Export Notebook As → HTML

Continue Your Progress Later 🔄

To resume your work:

Launch Binder again
Click Upload button
Upload your saved .ipynb file
Continue where you left off!

📤 Submission Requirements

For Assignment 5, submit TWO files to UC Davis Canvas:

📄

HTML/PDF Report

Your completed assignment with all calculations and analysis

💾

.ipynb File

Your notebook code as backup

Due Date: Check Canvas for assignment deadline

🎯 Learning Objectives

By the end of this week, you will be able to:

✅ Calculate required sample sizes for different precision levels

✅ Construct confidence intervals for means and proportions

✅ Understand the relationship between confidence level and margin of error

✅ Use normal distribution functions for statistical inference

✅ Apply z-score standardization to compare different datasets

✅ Design studies with appropriate statistical power

❓ Need Help?

📧 Contact Information

Mohammadreza Narimani
📧 mnarimani@ucdavis.edu
🏫 Department of Biological and Agricultural Engineering, UC Davis

🔧 Common Issues

Binder won't load? Try refreshing or clearing browser cache
Sample size too large? Check your formula and parameter values
Confidence interval wrong? Verify z-value and standard error calculations
qnorm() error? Make sure probability is between 0 and 1

📚 Additional Resources

Sample Size Theory: Review power analysis and effect size concepts
R Documentation: Use ?qnorm for help with normal functions
Practice: Try different confidence levels to see effects on sample size

🌟 Tips for Success

💡 Best Practices

Use ceiling() - Always round up sample sizes to whole numbers
Check your z-values - 1.96 for 95%, 1.645 for 90%, 2.576 for 99%
Understand trade-offs - Higher confidence = larger sample size
Verify calculations - Double-check formulas and parameter values
Think practically - Consider cost and feasibility of sample sizes

⚡ Key Formulas

n = z²p(1-p)/d² Sample size for proportions

x̄ ± z(s/√n) Confidence interval for means

z = (x-μ)/σ Z-score standardization

SE = s/√n Standard error

🎉 Ready to Start?

Click the Binder badge below to launch Week 5!

Launch Week 5 Interactive Environment

Happy sampling and estimating! 📊🌾

Last updated: October 2025 | PLS 120 - Applied Statistics in Agriculture | UC Davis
Week 5: Sampling and Estimation

📊 Week 5: Sampling and Estimation