Inferential Statistics Lecture Overview

Oct 2, 2024

Lecture on Inferential Statistics

Recap from Last Lecture

  • Continued with the example of testing the average weight of apples.
  • Corrected the formula for inferential statistics.

Testing the Average Weight of Apples

  • Hypothesis: Average weight of apples is 150g.
  • Significance Level: Discussed in context of hypothesis testing.
  • Excel Note: Excel doesn’t have a direct one-sample T-Test function; requires manual formula input.

Steps in Hypothesis Testing

  1. T-Statistic Calculation:
    • Example with apple weights.
    • Correct data range used: A1 through A10.
  2. P-Value Calculation:
    • P-value: Probability of obtaining the observed results.
    • Formula adjustment needed for degrees of freedom.
  3. Decision Rule:
    • Compare P-value with Alpha (0.05).
    • If P-value < 0.05, reject the null hypothesis.

Conclusion from Example

  • Result: Do not reject the null hypothesis.
  • Practical interpretation: Average weight of apples is 150g.

Confidence Intervals

  • Definition: Range that is likely to contain the population parameter.
  • Example: 95% confidence interval for apple weights.
  • Calculation Steps:
    • Critical value and bounds (lower & upper).
    • Interpretation: Average apple weight falls within these bounds.

Independent Two-Sample T-Test

  • Compare averages between two groups (e.g., apples from two farms).
  • Null Hypothesis: Weights are equal.
  • P-Value Calculation:
    • Use Excel to obtain P-value.
    • Decision: Reject null hypothesis if P-value < 0.05.

Paired T-Test

  • Used for repeated measures (before and after scenarios).
  • Hypothesis Testing Steps:
    • Similar formula to independent test but adjusted for paired data.
    • Compare results with critical P-value.
    • Decision: Reject null if P-value is less than the significance level.

Project 1 Overview

  • Real-world business scenarios involving statistical analysis.
  • Structure: Group assignment; includes analysis and interpretation tasks.
  • Hints Section: Provides guidance on statistical methods to apply.

Key Tasks in Project

  1. Store Revenue Analysis: Calculate statistical measures (mean, median, etc.).
  2. Employee Satisfaction: Construct confidence intervals.
  3. Defect Rate Testing: Use Z-test for proportions.
  4. Customer Age & Purchases: Chi-square test for independence.
  5. Comparing Profit Margins: Two-sample T-Test.
  6. Paired T-Test Scenario: Analyze before and after conditions.

Final Notes

  • Use Excel for computations; submit findings in a Word document.
  • Group work emphasized; form groups for project collaboration.