Conditions

Conditions

1. one-sample mean

   • normal sampling distribution
     • SRS with replacement
       • Known sigma SD

2. one-sample proportion

   • binomial
     • SRS with replacement
       • normal
         • np-hat >= 15, nq-hat >=15

3. two-sample paired sample means

   • BOTH samples distributions are normal
     • makes the difference sampling distribution normal
   • BOTH samples were SRS w replacement

4. independent two-sample means

   • both samples SRS w replacement
     • both normal sampling distributions
       • pops both normal or both samples CLT
         • df=min(n1-1, n2-1)

5. two-sample proportions

   • Independent
     • both sampling distributions are NORMAL
       • both samples are SRS w replacement
       • >= 5 failures AND >= successes

6. multiple means

   • All samples are independent
     • ALL samples were taken via SRS or Randomized Design
       • Population distribution are approx. Normal
         • Constant variance across populations
           • df=K-1, N-K
           • scatterplot or residual plot (same as constant variance of Y across X of regreesion condition
             • or strip chart
         • QQ plot of residuals

7. regression

   • Y observations are independent
     • Linear relationship between Y and X
       • Y follows a Normal distribution for EACH x
         • Constant variance of Y across X
           • scatterplot show equal points randomly spread above and below horizontal (residual)
             • random 'scatter' or band of residuals (i.e. the same 'good' residual plot will meet both the linearity assumption and the constant variance assumption).
           • df=n-2
         • QQ plot of residuals
       • look if least squares regression line is good predictor , Scatterplot or residual plot
     • SRS with replacement, one y doesn't affect another

8. binomial

   • 2 outcomes
     • Independent trials
       • fixed number of trials
         • fixed probability of success
           • SRS with replacement ensures

9. sampling distribution

   • Normal population
   • sample >=50 (CLT)

10. Z confidence intervals

    • SRS with replacement
      • normal sampling distribution
        • known sigma SD

11. t confidence intervals

    • SRS with replacement
      • normal sampling distribution
        • df=n-1