# Mastering Statistical Inference: Estimation & Testing
> Learn key concepts of statistical inference, including point and interval estimation, confidence intervals, and hypothesis testing with worked examples.

Tags: statistical-inference, hypothesis-testing, confidence-interval, data-analysis, statistics-tutorial, z-test, null-hypothesis
## What is Statistical Inference?
* Process of using data analysis to infer properties of an underlying population probability distribution.
* Draws conclusions about a large population based on a smaller sample.

## Point vs. Interval Estimation
* **Point Estimation:** A single value (e.g., Sample Mean x̄) used to estimate the population parameter (μ).
* **Interval Estimation:** A range of values (Confidence Interval) within which the parameter is expected to lie.

## Confidence Intervals (CI)
* Proposes a range of plausible values for an unknown parameter.
* Example: For a 95% CI, we expect 95 out of 100 intervals from different samples to contain the true mean.

## Example: Finding 95% CI
* **Problem:** n=64, x̄=50, σ=8.
* **Standard Error (SE):** 8 / √64 = 1.0.
* **Margin of Error:** 1.96 * 1.0 = 1.96.
* **Result:** 50 ± 1.96 = [48.04, 51.96].

## Hypothesis Testing Basics
* **Null Hypothesis (H₀):** Statement of no effect or difference.
* **Alternative Hypothesis (H₁):** Statement trying to be proven.
* **Type I Error (α):** Rejecting H₀ when it is true (False Positive).
* **Type II Error (β):** Failing to reject H₀ when it is false (False Negative).

## Example: One-Sample Z-Test
* **Claim:** μ = 100. Sample: n=36, x̄=104, σ=12, α=0.05.
* **Test Statistic (Z):** (104 - 100) / (12/√36) = 4 / 2 = 2.0.
* **Decision:** Since Z (2.0) > 1.96, Reject H₀.
---
This presentation was created with [Bobr AI](https://bobr.ai) — an AI presentation generator.