Unit 7: Inference for Quantitative Data (Means) Study Guide Flashcards

What is sampling variability?

the natural variation between a sample mean and the population mean, also called sampling error.

Why is sampling variability important?

It reminds us that a sample mean is only an estimate of the population mean and will not perfectly match the true value.

What are the conditions for constructing a confidence interval for a population mean?

- Random: randomly selected/assigned

- Independent: n < .1N (not necessary for experiments).

- Normality: If the population is normal, any sample size is okay; otherwise, n ≥ 30 (Central Limit Theorem). If population is not stated normal and n is not ≥ 30, create a box plot and check for major outliers and skewness.

What is the formula for a confidence interval for a population mean?

(replace the z with t)

How do you interpret a confidence interval?

"We are ___% confident that the true population mean (context) is between (lower bound) and (upper bound)."

What is the formula for degrees of freedom in a t-interval

df = n - 1

What are the hypothesis in a significance test for a population mean

(H₀): 𝜇 = some value

(Hₐ): 𝜇 >, 𝜇 < or 𝜇 ≠ μ some value

What is the test statistic formula for a one-sample t-test

How do you determine the p-value in a t-test?

Use the tcdf function on a calculator to find the probability of obtaining a t-score as extreme or more extreme. or use t-test stat test.

How do you interpret a significance conclusion?

- If p-value < α, reject H₀ → Sufficient evidence for Hₐ

- If p-value ≥ α, fail to reject H₀ → Not enough evidence for Hₐ

What is the formula for a confidence interval for the difference of two means?

What are the conditions for a two-sample t-interval

- Two random samples

- Independent: n1 < .1N1, n2 < .1N2. not necessary for experiment.

- Normal: n1 ≥ 30, n2 ≥ 30; or check for outliers/skewness

How do you interpret a confidence interval for the difference of two means?

"We are ___% confident that the true difference between the population means is between (lower bound) and (upper bound)."

What are the hypothesis in a two-sample t-test?

- H₀: μ1 - μ2 = 0

- Hₐ: μ1 − μ2 is >, <, or ≠ 0

What is the test statistic for a two-sample t-test?

How do you determine the p-value for a two-sample t-test?

Use tcdf with the calculated t-score and degrees of freedom OR use t-test in stat-test.

How do you interpret the results of a two-sample t-test?

- If p-value < α, reject H₀ → Sufficient evidence for Hₐ

- If p-value ≥ α, fail to reject H₀ → Not enough evidence for Hₐ

What is a Type 1 error?

Rejecting Ho when it is actually true.

What is a Type 2 error?

Failing to reject Ho when it is actually false.

What is power?

The probability of correctly rejecting a false null hypothesis (increases with larger sample size).