Exam 3 Review: Hypothesis Testing Concepts

This set of flashcards covers key vocabulary and concepts related to hypothesis testing as outlined in the lecture notes, providing definitions that will aid in exam preparation.

Hypothesis

A statement about parameters, not statistics.

Null Hypothesis (Ho)

The assumption that nothing has changed or there is no relationship; always involves '='.

Alternative Hypothesis (Ha)

A statement that something has changed; involves symbols like '>', '<', or '=/='.

Significance Level (alpha, α)

The probability of making a Type 1 error; the threshold for rejecting the null hypothesis.

Test Statistic

A standardized value that compares observed data to a probability distribution.

Critical Value

A threshold determined from statistical tables that defines the rejection region.

Degrees of Freedom (df)

A value used in statistical tests that indicates the number of independent values.

P-value

The probability of observing the data, or something more extreme, under the null hypothesis.

Type 1 Error

Rejecting the null hypothesis when it is actually true.

Type 2 Error

Failing to reject the null hypothesis when it is actually false.

Confidence Interval for Differences

An estimate of a range of values within which the true difference in population means lies.

Two-tailed Test

A hypothesis test where the alternative hypothesis is not directional (involves ≠).

One-tailed Test

A hypothesis test where the alternative hypothesis is directional (involves only '>' or '<').

Z-test

A statistical test used to determine if there is a significant difference between sample and population means.

T-test

A statistical test used for small sample sizes to compare the means of two groups.

Chi-square Test

A statistical test to determine if there is a significant association between categorical variables.

Goodness of Fit

A Chi-square test to assess if observed data matches expected data.

Independence Test

A Chi-square test to evaluate if two variables are independent.

Standard Normal Distribution

A normal distribution with a mean of 0 and a standard deviation of 1.

Significant Difference

When the confidence interval does not include zero indicating a statistically significant result.

Reject the Null

To conclude that there is enough evidence to support the alternative hypothesis.

Fail to Reject the Null

To conclude that there is not enough evidence to support the alternative hypothesis.

T-distribution

A probability distribution that is symmetric and resembles the normal distribution, but has heavier tails.

Chi-square Statistic

A measure used in Chi-square tests to quantify how much observed frequencies differ from expected frequencies.

Expected Count

The frequency we expect in each category, assuming the null hypothesis is true.

Null Hypothesis Acceptance

We never accept the null; we only fail to reject it.

Alternative Hypothesis Evidence

Decisions in hypothesis testing are always about the alternative hypothesis.

Rejection Region

The area in a statistical test where we would reject the null hypothesis.

Normal Distribution Table

A table used to find probabilities associated with the standard normal distribution.

Sample Size (n)

The number of observations or data points in a statistical sample.

Significance Test

A procedure to determine if a hypothesis can be rejected based on sample data.

Hypothesis Testing Steps

Formulate hypotheses, determine significance level, compute test statistic, make decision based on critical value or p-value.

Conclusions in Hypothesis Testing

If we reject the null, conclude that something has changed; if we fail to reject, we do not conclude anything has changed.

Change Symbol in Hypotheses

The symbol used in the alternative hypothesis that indicates the direction of the change.