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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.