EXST 2201 NOTES

Population Information

essential for making more informed, reliable decisions

Statistical Decision Making

based on data from a larger sample or population, offering a more accurate picture for decision- making

Anecdotal

based on a small group of individuals (less reliable)

Stastical Inference

Using statistical methods to infer population parameters based on sample statistics.

Process of Statistical Inference

Theorize, Analyze, and Infer

Theorize

Use probability information (theoretical study of the population).

Analyze

Analyze sample data

Infer

make inferences about the population using methods like confidence intervals or hypothesis testing

Population Mean

The most important value we want to know (e.g., average height of males vs. females).

Sample Average (x̄)

A statistic that helps estimate the population mean, called a "point estimate."

Normal Distribution

Most data points lie close to the mean, so the population mean provides a useful, easy-to-understand summary.

Why Population Mean Matters

Understanding it allows for meaningful comparisons (e.g., comparing averages between groups).

Point Estimate of the Population Mean

The sample average is the best estimate for the population mean (μ), but it's rarely exactly the same as the population mean due to randomness.

General Methods of Solving Problems

• Step A: Abstract - Identify relevant information and simplify the problem into a statistical model.

  • Process of Abstraction: Extract essential data from the real-world scenario and ignore irrelevant details.

• Step 1: Theorize - Use probability information.

  • Write Hypotheses: Define the statistical hypotheses (needed for hypothesis testing).

  • Draw Schematic Curve: Visualize the situation with a probability curve.

• Step 2: Analyze - Use sample data (descriptive statistics) to get numerical values.

• Step 3: Infer - Use statistical inference to make conclusions about the population using sample data.

Confidence interval

A range of values around the sample mean that provides an estimate for the population mean.

Hypothesis Testing

• tests a claim or hypothesis about the population mean based on sample data.

• Involves comparing the sample data against a proposed population mean to determine if the claim is reasonable.