Statistical Inference Lecture Notes

Introduction to Statistical Inference

• Definition: The process of making judgments about a population based on sampling data.
• Importance: Vital for decision-making in various fields, including business, economics, and health sciences.

Types of Statistical Inference

1. Estimation
   • Point Estimation: Provides a single value as an estimate of a population parameter.
   • Interval Estimation: Provides a range of values (interval) within which the parameter is expected to lie with a certain degree of confidence.
2. Hypothesis Testing
   • Used to assess the evidence against a null hypothesis.
   • Involves making decisions using sample data.

Confidence Intervals

• Definition: A range of values used to estimate the true value of a population parameter.
• Components:
  • Point Estimate: The sample statistic that serves as the best estimate of a population parameter.
  • Margin of Error: Reflects the amount of random sampling error in the estimate.
• Common Confidence Levels: 90%, 95%, and 99%.

Hypothesis Testing

• Steps in Hypothesis Testing:
  1. State the Hypotheses: Formulate both the null and alternative hypotheses.
  2. Choose a Significance Level (α): Common levels are 0.05, 0.01, or 0.10.
  3. Select the Test Statistic: Depends on the sample size and the type of data.
  4. Decision Rule: Determine the criteria for rejecting the null hypothesis.
  5. Perform the Test: Calculate the test statistic using sample data.
  6. Conclusion: Decide whether to reject or fail to reject the null hypothesis.
• Types of Errors:
  • Type I Error: Rejecting a true null hypothesis (false positive).
  • Type II Error: Failing to reject a false null hypothesis (false negative).

Key Terms and Concepts

• Population: The entire group that is the subject of a statistical study.
• Sample: A subset of the population used to represent the whole group.
• Parameter: A numerical characteristic of a population.
• Statistic: A numerical characteristic of a sample.

Practical Applications

• Business: Market analysis, quality control, financial forecasting.
• Health Sciences: Clinical trials, epidemiology, public health policy.
• Economics: Policy assessment, economic forecasting, resource allocation.

Conclusion

• Statistical inference plays a crucial role in analyzing data and making informed decisions based on sample data.