Set 1 – Core Ideas (Ch. 8–10)

Card 1
Q: What is a Z‑score?
A: Z = (value − mean) / SD. It tells how many standard deviations a value is above or below the mean.

Card 2
Q: What is a confidence interval (CI)?
A: An interval (two numbers) that likely contains the true parameter (p, μ, σ, or σ²) with a certain confidence level (like 95%).

Card 3
Q: What is α (alpha)?
A: The significance level. α = 1 − confidence level. Example: 95% confidence → α = 0.05.

Card 4
Q: What is a p‑value (in words)?
A: The probability (between 0 and 1) of getting results as extreme as your sample (or more) if H₀ is true.

Card 5
Q: Decision rule using p and α?
A: If p ≤ α → Reject H₀ (statistically significant).
If p > α → Fail to reject H₀.

Set 2 – Symbols

Card 6
Q: What is p vs p̂ ?
A: p = true population proportion.
p̂ (“p‑hat”) = sample proportion = x/n.

Card 7
Q: What is μ vs x̄ ?
A: μ = true population mean.
x̄ = sample mean (average of sample).

Card 8
Q: What is σ vs s ?
A: σ = population standard deviation.
s = sample standard deviation.

Card 9
Q: What is df (degrees of freedom) for t and χ²?
A: df = n − 1.

Set 3 – Which Test / Interval?

Card 10
Q: When do I use 1‑PropZInt?
A: For a confidence interval for a proportion p. Wording: “proportion”, “percentage”, “x out of n”.

Card 11
Q: When do I use TInterval?
A: For a confidence interval for a mean μ when σ is unknown. Wording: “mean”, “average”.

Card 12
Q: When do I use 1‑PropZTest?
A: For a hypothesis test about a proportion p. Wording: “test the claim about the proportion / percentage…”

Card 13
Q: When do I use TTest?
A: For a hypothesis test about a mean μ with sample data. Wording: “test the claim that the mean/average…”

Card 14
Q: When do I use chi‑square (χ²) in Chapter 9–10?
A: For confidence intervals or tests about σ or σ² (standard deviation / variance).

Set 4 – Calculator Buttons

Card 15
Q: Button for CI for proportion p?
A: STAT → TESTS → 1‑PropZInt.

Card 16
Q: Button for CI for mean μ?
A: STAT → TESTS → TInterval (Data or Stats).

Card 17
Q: Button for test of proportion p?
A: STAT → TESTS → 1‑PropZTest.

Card 18
Q: Button for test of mean μ?
A: STAT → TESTS → TTest (never ZTest in this class).

Card 19
Q: Button to get Z_{α/2}?
A: 2nd → VARS → 3:invNorm (use left‑side area).

Card 20
Q: Button to get t_{α/2,df}?
A: 2nd → VARS → 4:invT (use left‑side area and df = n−1).

Card 21
Q: Button for P(Z > a) (right‑tail area)?
A: 2nd → VARS → 2:normalcdf( a, 1E99 ) for standard normal.

Set 5 – Confidence Intervals Details (Ch. 9)

Card 22
Q: Formula for sample proportion p̂ ?
A: p̂ = x / n, where x = # successes, n = sample size.

Card 23
Q: General CI form for p (concept)?
A: p̂ ± Z_{α/2}·√[p̂(1−p̂)/n].
(But in practice, use 1‑PropZInt.)

Card 24
Q: General CI form for μ (concept)?
A: x̄ ± t_{α/2,df}·(s/√n).
(Use TInterval.)

Card 25
Q: What does a 95% CI for p mean in words?
A: We are 95% confident that the true proportion p is between the two CI bounds.

Card 26
Q: What does a 95% CI for μ mean in words?
A: We are 95% confident that the true mean μ is between the two CI bounds.

Card 27
Q: Formula for sample size n for a proportion?
A: ( n = \dfrac{p̂(1 - p̂)(Z_{\alpha/2})^2}{E^2} ).
If no p̂ given, use 0.5 and round n UP.

Card 28
Q: CI for variance σ² using chi‑square (just structure)?
A:
Lower: (n−1)s² / χ²_{1−α/2,df}
Upper: (n−1)s² / χ²_{α/2,df}.

Card 29
Q: How to get CI for σ from CI for σ²?
A: Take square roots of lower and upper bounds.

Set 6 – Hypothesis Testing Structure (Ch. 10)

Card 30
Q: What MUST I always write in a hypothesis test (4 items)?
A: 1) H₀ and H₁
2) Name of test (1‑PropZTest or TTest)
3) p‑value (0–1)
4) Conclusion sentence in context.

Card 31
Q: Rule for H₀ and H₁ symbols?
A: H₀ always has “=” (p = p₀ or μ = μ₀).
H₁ uses <, >, or ≠ depending on wording.

Card 32
Q: Wording → symbol: “less than 10”?
A: H₁: parameter < 10.

Card 33
Q: Wording → symbol: “greater than 0.4”?
A: H₁: parameter > 0.4.

Card 34
Q: Wording → symbol: “different from 50”?
A: H₁: parameter ≠ 50.

Card 35
Q: What does “statistically significant” mean?
A: p ≤ α, so we reject H₀.

Set 7 – Common Mistakes to Avoid

Card 36
Q: What happens if my written p‑value is not between 0 and 1?
A: It’s wrong. Your professor gives 0 credit for that p‑value.

Card 37
Q: Should I ever use ZTest for a mean in this class?
A: No. Use TTest (σ is unknown).

Card 38
Q: When α is not given in a test question, what do I use?
A: Default α = 0.05 (5%).

Card 39
Q: For sample size n formula, how do I round?
A: Always round n UP to the next whole number.