Hypothesis Testing and the Central Limit Theorem

Sampling Distribution

Distribution of sample means from repeated samples.

Confidence Level

Probability that the true parameter lies within the interval.

Causation

Relationship where one variable directly affects another.

Modus Tollens

Logical reasoning used to reject hypotheses.

Percentile

Value below which a percentage of data falls.

Type 1 Error

Rejecting null hypothesis when it is true.

Type 2 Error

Not rejecting null hypothesis when it is false.

Statistical Significance

Result unlikely due to chance at specified confidence level.

Alpha Level (α)

Threshold for determining statistical significance.

Random Sampling

Selecting samples where each member has equal chance.

Unimodal Distribution

A distribution with a single peak.

Bimodal Distribution

A distribution with two distinct peaks.

Central Limit Theorem

Sample means approach normal distribution as sample size increases.

Sample Mean

Average value calculated from a sample.

Statistical Hypothesis

Testable statement about population parameters.

Null Hypothesis (H0)

Proposition stating no meaningful relationship exists.

Resampling

Technique to create sampling distributions from samples.

Inference

Conclusion drawn from evidence and reasoning.

Population Parameter

Characteristic or measure of an entire population.

Sample Statistic

Characteristic or measure computed from a sample.

Exam Scores Example

Illustrates Central Limit Theorem with student scores.

Chance

Random variation affecting sample outcomes.

Assumption in Hypothesis Testing

Assuming sample comes from the original population.

Conventional Significance Level

Statistical difference not significant if error exceeds 5%.

Null Hypothesis Example

No difference in strength between two groups.

Combining Samples

Assuming null hypothesis to create a larger sample.

Probability of Difference

Likelihood of observing differences due to chance.