Chapter 9: Hypothesis Testing

This set of flashcards covers key concepts and vocabulary from Chapter 9 on Hypothesis Testing, helping you review important terms and definitions.

Hypothesis Testing

The process of making statistical inferences based on sample data.

Null Hypothesis (H0)

The hypothesis that there is no effect or difference, tested directly.

Alternative Hypothesis (H1)

The hypothesis that proposes a difference or effect exists.

Sampling Error

The error that occurs when a sample does not represent the population accurately.

Confidence Interval

A range of values derived from sample statistics that is likely to contain the true population parameter.

Z-distribution

A normal distribution used in hypothesis testing when the population standard deviation is known.

Alpha Level (α)

The threshold for rejecting the null hypothesis, commonly set at 0.05.

Critical Value (c.v.)

The z-score that corresponds to the alpha level for hypothesis testing.

Z-score

A measure of how many standard deviations an element is from the mean.

P-value

The probability of obtaining a sample statistic as extreme or more extreme than the observed value under the null hypothesis.

One-tailed Test

A hypothesis test used to test if a parameter is greater than or less than a certain value.

Two-tailed Test

A hypothesis test used to determine if a parameter is different from a certain value, in either direction.

T-distribution

A probability distribution used when the population standard deviation is unknown and the sample size is small.

Degrees of Freedom (df)

The number of independent values in a statistical calculation, impacting the t-distribution shape.

Central Limit Theorem

The theorem that states that the distribution of sample means approaches a normal distribution as sample size increases.

Standard Error (SE)

An estimate of the standard deviation of the sample mean distribution.

Critical Region

The area in the tail(s) of the distribution where the null hypothesis is rejected.

Significance Level

The probability of making a Type I error, rejecting a true null hypothesis.

Type I Error

The error made when rejecting a true null hypothesis.

Type II Error

The error made when failing to reject a false null hypothesis.

Effect Size

A measure of the strength of the relationship between two variables.

Null Hypothesis Testing

The framework used to determine if there is enough evidence to reject the null hypothesis.

T-test

A statistical test used to compare the means of two groups.

R Software

A programming language used for statistical computing and graphics in hypothesis testing.

Sample Mean (x̄)

The average value of a sample.

Population Parameter (μ)

A fixed value that represents a characteristic of a population.

Standard Deviation (σ)

A measure of the amount of variation or dispersion in a set of values.

95% Confidence Interval

An interval estimate that has a 95% chance of containing the true population parameter.

Sampling Distribution

The theoretical distribution of sample means based on repeated sampling.

Hypothesis Test Procedures

The steps taken to conduct a hypothesis test including formulating hypotheses, calculating test statistics, and making decisions.

Proportion Test

A statistical test used to compare sample proportions to a hypothesized population proportion.

Z-score for Proportions

A method for standardizing proportions to test hypotheses about population proportions.

Normal Distribution

A probability distribution that is symmetric about the mean, representing the distribution of many types of data.

Effect of Sample Size on t-distribution

As sample size increases, the t-distribution approaches the normal distribution.

R Functions for Hypothesis Tests

Commands in R, like t.test, used for performing hypothesis tests.

Multiple Comparisons

Statistical methods for evaluating multiple hypotheses simultaneously.

Confidence Interval Interpretation

Deciding how confident one is that the interval includes the true population parameter.

Random Sampling

The process of selecting a subset of individuals from a population where each individual has an equal chance of being chosen.

Random Variation

The natural fluctuations in data that arise due to chance.

Statistical Significance

A determination that an observed effect in data is not likely due to chance.

Non-directional Hypothesis

An alternative hypothesis that does not specify the direction of the expected difference.

Directional Hypothesis

An alternative hypothesis predicting the direction of the expected difference.

Sampling Bias

A systematic error due to a non-random sample that does not represent the population.

Statistical Inference

The process of using data from a sample to make conclusions about a population.

Reporting Results

The process of communicating the results of hypothesis tests, including p-values and conclusions.

Data Visualization Tools

Graphical representations of data used to enhance understanding of statistical results.

Figure Illustrations

Diagrams and charts that visually represent statistical concepts discussed in hypothesis testing.

Statistical Software Packages

Programs like R that provide tools for statistical analysis and hypothesis testing.

ANOVA (Analysis of Variance)

A statistical technique for comparing means among three or more groups.

Practical vs. Statistical Significance

Practical significance considers the real-world importance of a result, while statistical significance assesses the likelihood that a result occurs by chance.

Sampling Methodologies

Different techniques used to select samples from a population for statistical analysis.