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Chapter 7: Probability and Samples: The Distribution of Sample Means,…
Chapter 7: Probability and Samples: The Distribution of Sample Means
Population normal or n > 30
Central Limit Theorem (CLT)- The sampling distribution normality as n increases
Foundation for inferential statistics
Estimates liklihood
Sampling Distribution- Spread of sample statistics
Standard Error (SE): SD of the sample means σM = σ / √n
Type 1 Error: Rejects the null hypothesis (H₀) when it is true le.g. not allowing a passenger with no weapon to board a plane
α (alpha)
β (beta)
Type II Error: Failing to reject the null hypothesis when it is false; allowing a person with a weapon to board a plane
Expected Value of M: Mean of sampling distribution (μ)
Distribution of Sample Means- A spread of means from all random samples of a specific size (n) from a population
Chapter 8: Introduction to Hypothesis Testing
Validates Claims
Proves validity
Assists in data driven decision making
Appropriate for education research and public health studies
Hypothesis Testing Process- Step 1- State Hypotheses
Step 2- Set Decision Criteria
Alpha level (α), commonly .05
Null:(H₀) No difference/distinction; Alternative: (H₁) There is an effect/distinction
Step 3: Collect Data and Compute Statistic
Step 4: Make a Decision; compare z/t value to critical region
Power- Probability of correctly rejecting H₀
Type 1 Error (α): rejecting H₀ when true
Type II Error (β): not rejecting H₀ when it's true
Chapter 6: Probability
Probability (p) -The likelihood of an occurrence. Scale from 0-1; 0-least likely- 1-most likely
p (event)= number of favorable outcomes/total number of possible outcomes
Types of Probability
Empirical Probability- Based on actual data or observation
Theoretical Probability: Based on known outcomes (coin toss)
Best used- Single-sample t-test
Comparing sample mean to known population mean
Independent Event: one event does not affect the probability of another e.g two coin tosses
Dependent Event:One event does affect the probability of the next e.g. drawing two cards without replacement
Unit Normal (Z-Table)- Determines the proportion of scores in normal distribution
Estimated Standard of M-Standard difference between a standard mean and a population mean
Values range from 0 (impossible) to 1 (certain)
Allows researchers to calculate proportion below/above a given z-score
Proportion below z-score
Random Sampling: equal chance of selection for entire population
Sampling with Replacement: selected individual returned to population before next selection; maintains constant probability
Ensures unbiased probability calculations