Chapter 7: Inference For Numerical Data Flashcards
When is the t-distribution used?
When the sample size is small and population standard deviation is unknown.
What are the conditions for using the t-distribution?
Independent observations and an approximately normal population.
What is paired data?
Data where observations are naturally matched, like before and after measurements.
What is the test statistic formula for a paired t-test?
T = (x̄_diff - 0) / (s_diff / √n)
What is the degrees of freedom for a paired t-test?
df = n - 1
What is the formula for a confidence interval using t-distribution?
x̄ ± t* × (s / √n)
When comparing two independent means, what test do you use?
Two-sample t-test.
What is the test statistic for two-sample t-test?
T = (x̄1 - x̄2) / sqrt(s1²/n1 + s2²/n2)
What are the hypotheses for a two-sample t-test?
H₀: μ₁ = μ₂ vs Hₐ: μ₁ ≠ μ₂
What is the formula for degrees of freedom in a two-sample t-test (simplified)?
df = min(n₁ - 1, n₂ - 1)
What is a Type I error?
Rejecting the null hypothesis when it is actually true.
What is a Type II error?
Failing to reject the null hypothesis when it is actually false.
What is the power of a test?
The probability of correctly rejecting a false null hypothesis (1 - β).
How can we increase the power of a test?
Increase sample size, reduce standard deviation, or raise α.
What is the effect size?
The magnitude of the difference you aim to detect.
What happens to power when sample size increases?
Power increases.
What is the margin of error in a confidence interval?
ME = t* × SE
When do we use a paired t-test?
When comparing means from the same group at different times or matched groups.
What distribution has thicker tails: t or normal?
The t-distribution.
What does a large p-value mean in hypothesis testing?
There is not enough evidence to reject the null hypothesis.
