The Bridge: Sampling Distributions
Sampling a whole group is impossible; instead, we sample. But, how does a sample represent the full population? The **Central Limit Theorem** explains it. This theorem says repeated sample means create a bell curve, centered on the true average. Build a sampling distribution now!
Population Info
True Mean (μ): 100
Sample Stats
Samples Drawn: 0
Last Mean (x̄): N/A
The Framework: Making a Decision
Imagine hypothesis testing as a courtroom. The **Null Hypothesis (H₀)** is the defendant, presumed "not guilty" (no change). The **p-value** represents the presented evidence. If the p-value falls below our "burden of proof" (the **significance level α**), we convict the null and reject it. Adjust the slider to set your α and then execute the test.
The Trade-Off: Type I & II Errors
Tests aren't flawless. Errors happen in two ways, and reducing one type frequently raises the other. This inherent compromise defines statistical analysis.
Type I Error (α)
False Positive
You reject H₀ when it's actually true.
(You conclude there's an effect when there isn't one)
Type II Error (β)
False Negative
You fail to reject H₀ when it's actually false.
(You miss an effect that truly exists)
The Estimate: Confidence Intervals
Rather than a binary "reject/fail to reject" in hypothesis testing, a confidence interval provides a span of likely values for the population parameter. It offers an estimate with an associated margin of error.
Standard Error (SE):
95% Confidence Interval:
The Toolbox: Choosing the Right Test
Here are a few rewritten options, all roughly the same length and conveying a similar meaning: * **Diverse inquiries call for diverse methods. This flowchart guides your selection between two core hypothesis test types.** * **The right tool depends on the question. This easy flowchart helps you pick between two prevalent hypothesis test approaches.** * **Varying questions, varying tools. Use this flowchart to help you choose between two of the most common hypothesis tests.**
What kind of data are you analyzing?