All Flashcards
What is a two-sample t-test?
A test to determine if the means of two independent groups are significantly different.
Define Null Hypothesis (Ho) in a two-sample t-test.
The hypothesis stating there is no difference between the means of the two populations being compared. (𝞵1 = 𝞵2)
Define Alternative Hypothesis (Ha) in a two-sample t-test.
The hypothesis stating there is a difference between the means of the two populations being compared (𝞵1 ≠ 𝞵2, 𝞵1 < 𝞵2, or 𝞵1 > 𝞵2).
What is a parametric test?
A statistical test that assumes the data is normally distributed and the variances of the groups are equal.
What is the 10% condition?
A condition that checks for independence by verifying that the population is at least 10 times the sample size.
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.