Hypothesis Testing Concepts part 2

These flashcards cover essential vocabulary and concepts related to hypothesis testing in statistics, derived from the lecture notes provided.

One-Sample Z-Test

A hypothesis test used when the population standard deviation (σ) is known.

One-Sample T-Test

A hypothesis test used when the population standard deviation is unknown; uses sample standard deviation.

Sample Mean (x̄)

The average of your sample data.

Population Mean (μ)

The claimed mean from the null hypothesis.

Population Standard Deviation (σ)

The standard deviation of the entire population.

Sample Size (n)

The number of data points in your sample.

Degrees of Freedom (df)

Calculated as n – 1; necessary for determining critical values in t-tests.

Z-Test Statistic

A standardized value that measures how far the sample mean is from the population mean assuming the null hypothesis is true.

T-Test Statistic

Similar to the z-test but used when the population standard deviation is unknown.

Critical Value

The cutoff point(s) that mark the rejection region in hypothesis testing.

p-value

The probability of observing a result as extreme as the test statistic under the null hypothesis.

Significance Level (α)

The pre-set probability cutoff for deciding whether to reject the null hypothesis.

Two-Tailed Test

A hypothesis test that considers both ends (tails) of the distribution.

One-Tailed Test

A hypothesis test that considers only one end (tail) of the distribution.

Type I Error (α)

Rejecting the null hypothesis when it is actually true (false positive).

Type II Error (β)

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

Power of a Test (1-β)

The probability of correctly rejecting the null hypothesis when it is false.

Independent Samples Test

A test comparing two unrelated groups.

Dependent (Paired) Samples Test

A test that compares two related measures.

Hypothesized Difference (μ₁ - μ₂)

The expected difference between two population means under the null hypothesis.

Sample Variance (s²)

The variance derived from the sample data.

Test Statistic Formula: Z-Test

z = (x̄ - μ) / (σ/√n) where σ is known.

Test Statistic Formula: T-Test

t = (x̄ - μ) / (s/√n) where σ is unknown.

z-Critical Value for α=0.05 (Two-Tailed)

±1.96.

z-Critical Value for α=0.05 (One-Tailed)

1.645.

t-Critical Value for α=0.05 (n=25, df=24, Two-Tailed)

≈ ±2.064.

Population Mean (μ)

The average of a whole population.

Significance Level (α=0.05)

Common threshold for testing significance.

Comparison of Exam Scores

An example of using an independent samples test.

Power Calculation

1 - β, the probability of correctly rejecting a false null hypothesis.

Null Hypothesis (H₀)

The statement being tested, typically a statement of 'no effect'.

Alternative Hypothesis (H₁)

The statement that indicates the presence of an effect.

Matched Pairs

Participants paired based on shared characteristics, often used in dependent samples tests.

Z-Test Conditions

Used when population SD is known and sample size is large (n > 30).

T-Test Conditions

Used when population SD is unknown; relies on sample SD.

Rejection Region

The area under the curve where the null hypothesis can be rejected.

Critical Region

The section of the curve that leads to rejecting the null hypothesis.

Z-Score

Standardized score indicating how many standard deviations an element is from the mean.

T-Distribution

The probability distribution that is used in t-tests; varies with degrees of freedom.

Research Hypothesis

The hypothesis that the researcher aims to support; usually corresponds to H₁.

Sampling Distribution

The probability distribution of a statistic obtained through a large number of samples drawn from a specific population.

Assumption of Normality

The assumption that the data follows a normal distribution, important for hypothesis testing.

Single-Sample Test

A hypothesis test comparing a sample mean to a known population mean.

Two-Sample Test

A hypothesis test comparing means from two different groups.

Comparison of Means

The statistical analysis of the differences between sample means.

Decision Rule

Guideline for deciding whether to reject H₀ based on critical values.

Standard Error

The standard deviation of the sampling distribution of the sample mean.

Sample Standard Deviation (s)

An estimate of the standard deviation of the sample.

Test of Means

A category of hypothesis tests focused on mean comparisons.

Hypothesis Testing Steps

Define hypotheses, compute test statistics, compare to critical values, make conclusions.

Sample Data

The collected data from which sample statistics are calculated.

Rejecting the Null Hypothesis

Making the conclusion that there is enough evidence to support the alternative hypothesis.

Failing to Reject the Null Hypothesis

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

Standard Normal Table

A table utilized to find the critical values associated with the standard normal distribution.

Central Limit Theorem

States that the distribution of sample means approaches a normal distribution as the sample size increases.

Variance

A measure of the distribution of data points in a data set.