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Unit 5: Random Var & Sampling Distribution - Coggle Diagram
Unit 5: Random Var & Sampling Distribution
Sampling Distributions
μ = population mean
p̂ = sample proportion
P = population proportion
x̄ = sample mean
Unbiased Estimator
μ = x̄ (when pop. mean = smaple mean) it's unbiased
The bigger the sample size the smaller the variability
Steps for Finiding Probability
P
lan:
Randomness (e.g SRS)
Normality(Check with Large Counts Condition or CLT)
Independence(Check with 10% Condition)
D
o: Draw the normal curve(Region Shaded) and calculate the probability
S
tate: What we're trying to find
C
onclude: Put your findings into context
Sampling Distribution of Sample Mean
Center
Spread
If 10% Condition is met:
Shape
If CLT is true than it's normal
Central Limit Theorem (CLT)
If the sample size is >= 30 than the distribution is normal no matter what
If stated the population distribution is normal than the sampling dist. will also be normal
Difference in Sample Mean
Center
Spread
If 10% Condition is met for both:
Shape
If the CLT of both sample size is met or it's stated both pop. dist. is normal than it's normal
Sampling Distribution of Sample Proportions
10% Condition
N > 0.1*n (When the population size is 10% greater than the sample size)
Large Counts Condition (Checking for Normality)
If np>10 & n(1-p)>10 then the dist. is normal
Difference in Sample Proportions
Shape
Check with:
If not they're not normal
Spread
If 10% Condition is met for both:
Center
Sampling Proportion = (# of success)/sample size
Binomial Distribution
Shape
If 10% Condition is met than it's normal
Center
Spread
If 10% Condition is met:
Sample Distribution
Center
Spread
If 10% condition is met, then we can use:
Shape
If 10% Condition is met than it's normal
