All Flashcards
What is the null hypothesis formula for two sample t-test?
H₀: μ₁ = μ₂ or H₀: μ₁ - μ₂ = 0
What is the alternative hypothesis formula for a two-tailed test?
Hₐ: μ₁ ≠ μ₂ or Hₐ: μ₁ - μ₂ ≠ 0
What is the alternative hypothesis formula for a left-tailed test?
Hₐ: μ₁ < μ₂ or Hₐ: μ₁ - μ₂ < 0
What is the alternative hypothesis formula for a right-tailed test?
Hₐ: μ₁ > μ₂ or Hₐ: μ₁ - μ₂ > 0
Explain the concept of random sampling in the context of a two-sample t-test.
Random sampling ensures that the samples are representative of the populations, allowing for valid inferences about the population means.
Explain the importance of the independence condition in a two-sample t-test.
The independence condition ensures that the observations in one sample do not influence the observations in the other sample, which is crucial for the validity of the test.
Explain how the Central Limit Theorem (CLT) applies to the Normal condition for a two-sample t-test.
If each sample size is sufficiently large (n ≥ 30), the sampling distribution of the difference in sample means will be approximately normal, even if the population distributions are not normal.
Explain why it is important to state and check conditions before conducting a two-sample t-test.
Checking conditions ensures the validity of the test results. If conditions are not met, the conclusions drawn from the test may be unreliable.
Explain the relationship between the p-value and the conclusion of a hypothesis test.
The p-value indicates the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true. A small p-value suggests evidence against the null hypothesis.
What are the differences between the null and alternative hypotheses?
Null Hypothesis: States there is no effect or difference. | Alternative Hypothesis: States there is an effect or difference.
What are the differences between a one-tailed and a two-tailed alternative hypothesis?
One-Tailed: Tests for a difference in a specific direction (greater than or less than). | Two-Tailed: Tests for a difference in either direction (not equal to).
What are the differences between stating the conditions and checking the conditions?
Stating the conditions: Listing the required assumptions (Random, Independent, Normal). | Checking the conditions: Verifying that these assumptions are met by the data or problem context.