Midterm 2 Cheat Sheet

Normal Distributions & Probability Prob. Dist. Curve ,6 σ n → n=( 2 , 4 ,6 σ ¿ 2 1. Center=μ=median 2. Dispersion=Spread= σ 3. Area Under Curve=1 Central Limit Theorem (CLT) Sampling distribution of xx will be approximately normal most of the time Margin of error=W/2 μ is unknown= t distribution Estimate CI for μ with μ ´x+ t S t is dependent on df=n-1 LECTURE 13 One Sample-Z test -t test Null Hypothesis: H0: μ= Alternative Hypothesis: H1: μ/ (One Tailed) ↑Δ=↓β ↑n=↓β Δ does not change as sample size (n) changes T2 error is usually made due to sample size not being large enough LECTURE 15 1. Hypotheses: H0 H1 2. Data IF sample size (n) is large enough. n≈30 ↑n=↓SD=↑Accuracy (because capturing more data with each SD/step from μ) LECTURE 11 Statistical Inference 1. Estimation=Pt. Estimate=xx 2. Hypothesis testing= Interval Estimate (CI) (Need sampling distribution of xx OR Population which we sample from to be NORMAL & sample size needs to be large enough) 68/95/99% CI: μ≠ (Two Tailed-more conservative=P-valueX2) Significance Level (α) probability of statistical significance P-Value the probability of getting the sample result or more extreme IF H0 is true P-value α Reject H0 (sufficient evidence) P-valueα Fail to reject H0 (insufficient evidence) Slightly ±.05 “marginally significant” xx, n, μ, α, σ OR S 3. Test Statistics x´−μ Z= σ √n x´−μ t= s √n 4. Assumptions: -SRS -Pop(N)=normal OR Distribution of xx=normal ´x− 1, 2 ,3 σ √n μ x´ + 1 , 2, 3 σ √n LECTURE 14 ....................................CONTINUED..........................................