Hypothesis Testing with Two Samples Flashcards
What is Degrees of Freedom (df) in statistics?
The number of values in a sample that are free to vary.
Define Pooled Proportion.
An estimate of the common proportion p1 and p2 in a two-sample test of proportions.
What is Standard Deviation?
The square root of the variance; it measures how far data values are from the mean. Notation: s for sample, σ for population.
What is a Variable (Random Variable)?
A characteristic of interest in a population; denoted by uppercase Latin letters (X, Y, Z,…). Values taken (x, y, z,…) are known only after the experiment.
How are variables in statistics different from those in algebra?
- The domain may be non-numeric. 2. You know the value of the variable only after performing the experiment.
What is the distribution used in comparing two population means with unknown standard deviations?
Student’s t-distribution (with degrees of freedom not pooled).
What is the random variable in a two-mean test (unknown SDs)?
X̄₁ - X̄₂
When comparing two population means with known standard deviations, what distribution is used?
Normal distribution.
What is the random variable for comparing two means with known SDs?
X̄₁ - X̄₂
What is the distribution used in comparing two independent population proportions?
Normal distribution.
What is the random variable for comparing two proportions?
p̂₁ - p̂₂
In a matched/paired samples test, how is the test statistic calculated?
By subtracting one measurement from the other to get a single difference variable.
What is the random variable in a matched/paired sample t-test?
The mean of the differences (d̄)
What distribution is used in matched/paired samples tests?
Student’s t-distribution with n - 1 degrees of freedom.
What conditions must be met for a paired t-test with a small sample (n < 30)?
The differences must follow a normal distribution.
What kind of samples are used in matched/paired designs?
Dependent samples drawn from the same set of objects.
