Statistics Review: Hypothesis Testing & Confidence Intervals

Vocabulary flashcards covering key symbols, hypotheses, confidence intervals, margins of error, p-values, and distributions from the lecture notes.

μ

Population mean: the average value of a population.

X̄

Sample mean: the average of observed sample data.

n

Sample size: the number of observations in a sample.

σ

Population standard deviation: the spread of values in the population.

S

Sample standard deviation: the spread of observed sample values.

Σ

Summation symbol: denotes the addition of a sequence of values.

σ²

Population variance: the average squared deviation from the population mean.

S²

Sample variance: the average squared deviation from the sample mean.

df

Degrees of freedom: the number of values free to vary in a calculation.

p

Population proportion: the proportion in the entire population.

P-bar

Sample proportion: the proportion observed in the sample.

α

Significance level: the threshold for determining statistical significance.

Hypothesis test

Procedure using sample data to determine the reliability of a claim about a population parameter.

Ho (Null hypothesis)

Statement of no effect or no difference; assumed true unless evidence suggests otherwise.

Ha (Alternative hypothesis)

Statement that there is an effect or difference; what you aim to show.

Confidence interval (CI)

A range around a sample estimate likely to contain the true population parameter; formula example: x̄ ± critical value × (σ/√n).

Margin of error (MOE)

Half-width of a confidence interval; indicates the amount of sampling error; larger MOE means less precision.

Point estimate

A single value that estimates a population parameter (e.g., x̄ estimates μ).

p-value

Probability, under Ho, of obtaining results as extreme as observed (or more); used to decide whether to reject Ho.

Distributions

Families of probability distributions (Normal, z, t, binomial, χ², F) describing how values are spread.

Critical value

Cutoff from a distribution used in test statistics and confidence intervals.

Confidence level

Probability that the interval contains the true parameter in repeated sampling (e.g., 95%).

Conclusion

Final step of a hypothesis test: state whether Ho is rejected or not based on p-value and α.

0.10 alpha

Significance level of 0.10; if p = 0.072, you would reject Ho since p ≤ α.

0.05 alpha

Significance level of 0.05; if p = 0.072, you would fail to reject Ho since p > α.