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MIDTERM II “CHEAT SHEET” For the normal distribution, you are either attempting to find P(-∞ to X) or P(-∞ to Z) given an X or Z value or X or Z given P(-∞ to X) or P(-∞ to Z) For the t distribution, you are also trying to find a probability or a value along the axis. P(-∞ to X) = P(<X) μ = mean; Population: δ = standard deviation; π = proportion X = mean; Sample: S = standard deviation; p = proportion FOR X FOR t FOR Z FOR P P(<X) = NORMDIST(x,mean,sd,True) P(<X) = TDIST(t,df,tails) P(<Z) = NORMSDIST(Z) P(<Z) = =NORMSDIST(Z) X = NORMINV(P(<X),mean,sd) t = TINV(P(<X),df) Z = NORMSINV(P(<Z)) Z = NORMSINV(P(<Z)) CHAPTER 6: THE NORMAL DISTRIBUTION CHANGING X SCALE TO Z SCALE: CHANGING Z SCALE TO X SCALE Z = (X-μ)/δ X = μ+z δ CHAPTER 7: SAMPLING AND SAMPLING DISTRIBUTION FOR THE MEAN X SCALE TO FIND X B A R Z SCALE TO FIND X B A R Z SCALE TO FIND THE MEAN PROPORTION σXbar = σ/√n σXbar = σ/√n σp = SQRT(π(1-π)/n) Xbar = μ + Zσ/√n Z = (Xbar – μ) / (σ/√n) Z = (p-π) / SQRT(π(1-π)/n) CHAPTER 8: CONFIDENCE INTERVALS CONFIDENCE INTERVAL OF THE MEAN (σ KNOWN) CONFIDENCE INTERVAL OF THE MEAN (σ UNKNOWN, S O USE S)) CONFIDENCE INTERVAL OF THE PROPORTI ON Xbar ± Zα/2 σ/√n Xbar ± tα/2 S/√n p ± Zα/2 SQRT(p (1-p)/n) Zα/2 for 90% CI = 1.64 Note; for TINV, the probability to enter is α, not α/2 Zα/2 for 95% CI = 1.96 Zα/2 for 99% CI = 2.58 ESTIMATING THE REQUI RED SAMPLE SIZE ( σ KNOWN) ESTIMATING THE REQUI RED SA MPLE SIZE ( σ UNKNOWN) ESTIMATING THE REQUI RED SA MPLE SIZE (PROPORTION) n = Z2α/2 σ2 / e2 NA n = Z2α/2 (π (1- π) / e2 CHAPTER 5: DISCRETE PROBABILITY DISTRIBU TION Binomial Distribution Pnumber_s = BINOMDIST(number_s, trials, probability_s, FALSE) Binomial mean = np Pnumber_s is the probability of a specific number of successes, not for P < a certain value. Binomial δ= SQRT(nμ*(1-μ)) Number_s = number of successes; trials=number of trials, probability_s = probability of success in a single trial Poisson Distribution Px = POISSON(x, mean, FALSE) Px is the probability of a specific number of successes, not for P < a certain value.