All Flashcards
What is the general form of the null hypothesis?
H₀: μ = μ₀, where μ is the population mean and μ₀ is the hypothesized population mean.
How to calculate the t-statistic for a one-sample t-test?
t = (x̄ - μ₀) / (s / √n), where x̄ is the sample mean, μ₀ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
How to determine the degrees of freedom (df) for a one-sample t-test?
df = n - 1, where n is the sample size.
What is the relationship between α and confidence interval?
Confidence Level = 1 - α. For example, α = 0.05 corresponds to a 95% confidence interval.
What is the significance level (α)?
The probability of rejecting the null hypothesis when it is actually true (Type I error).
Define the null hypothesis (H₀).
A statement of no effect or no difference, which we are trying to disprove. Expressed as H₀: μ = μ₀.
Define the alternative hypothesis (Hₐ).
The opposite of the null hypothesis. It is what we are trying to find evidence for (μ ≠ μ₀, μ < μ₀, or μ > μ₀).
What is a one-sample t-test?
A test used to compare a sample mean to a known or hypothesized population mean when the population standard deviation (σ) is unknown.
What is the rejection region?
The area under the t-distribution curve where, if our sample statistic falls, we reject the null hypothesis.
What are the differences between a one-tailed and a two-tailed t-test?
One-tailed: Tests for a directional difference (μ < μ₀ or μ > μ₀). Rejection region is on one side of the distribution. | Two-tailed: Tests for any difference (μ ≠ μ₀). Rejection region is on both sides of the distribution.
What are the differences between using a t-test and a z-test?
T-test: Used when the population standard deviation (σ) is unknown and estimated from the sample. | Z-test: Used when the population standard deviation (σ) is known.
What are the differences between the null and alternative hypotheses?
Null Hypothesis: A statement of no effect or no difference (μ = μ₀). It is what we are trying to disprove. | Alternative Hypothesis: The opposite of the null hypothesis, what we are trying to find evidence for (μ ≠ μ₀, μ < μ₀, or μ > μ₀).
What are the differences between Type I and Type II errors?
Type I Error: Rejecting the null hypothesis when it is true (false positive). Probability is α. | Type II Error: Failing to reject the null hypothesis when it is false (false negative). Probability is β.