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Unit 8 Hypothesis Testing - Coggle Diagram
Unit 8 Hypothesis Testing
Hypothesis
Definition: A claim or statement about a population property.
Hypothesis Testing
Purpose: Test the claim or statement, such as the average starting salary for CS graduates being $30,000/year.
Statistical Reasoning
Approach: Distinguish between likely and unlikely results by analyzing the sample set.
Central Limit Theorem (CLT)
Statement: With a sufficiently large sample size, the distribution of sample means will approximate normality, irrespective of the population distribution's shape.
Components of a Formal Hypothesis Test
Null Hypothesis (H0): Tested statement, includes conditions of equality (=, ≥, ≤).
Stating Your Hypothesis: If you wish to support your claim, it becomes the alternative hypothesis (H1).
Alternative Hypothesis (H1): True if H0 is false, includes conditions of inequality (≠, <, >).
Critical Value
Defined as the value(s) that separate the critical region from values that do not lead to H0 rejection.
Types of Error
Type I Error (α): Rejecting H0 when it is true.
Type II Error (ß): Failing to reject H0 when it is false.
Control: α and n choices impact Type I and II error risks.
Controlling Type I and Type II Errors
Relationship: Adjusting α and n affects the likelihood of Type I and II errors.
Strategy: Use the largest α tolerable, choose smaller α and larger n if Type I error consequences are severe.
Conclusions in Hypothesis Testing
Always test the null hypothesis with possible outcomes being either to fail to reject H0 or to reject H0.
Types of Tests
Two-tailed, Left-tailed, Right-tailed Tests: Determined by the direction of the hypotheses being tested.
Examples of Hypothesis Testing
Various real-world applications, such as testing new tire life, evaluating packaging quality, and examining battery capacity.