All Flashcards
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.
Explain the concept of the Central Limit Theorem (CLT) in the context of t-tests.
If the sample size (n) is at least 30, the sampling distribution of the sample mean is approximately normal, allowing us to use the t-distribution.
Explain the importance of random sampling in a t-test.
Random sampling ensures that the sample is representative of the population, allowing for valid inferences about the population mean.
Explain the independence condition in the context of t-tests.
The population size must be at least 10 times the sample size (10n) to ensure that the observations are independent.
Explain the relationship between the p-value and the significance level (α).
If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.
Explain Type I error.
Rejecting the null hypothesis when it is true. The probability of committing a Type I error is equal to the significance level (α).
Explain the purpose of checking conditions before performing a t-test.
Checking conditions (randomness, independence, normality) ensures that the assumptions underlying the t-test are met, making the results of the test valid and reliable.
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.