Name:_____________________
Z-score, CDF of sample means

x→Z-score→CDF ***

Set mean μ=100  SD σ=10
 for educational purposes we will assume we know the population's parameters.

SEM (standard error of the mean): the SD of the population of all sample means. 
                                                           (of a particular n)
 i.e. the SD of the "sampling distribution of the mean"
 = σ / √n

Sample size n=10 → SEM=(σ/√n)=_________

   Probability that a sample's mean would be this much or greater:
x̄ = 101   z=______   P(x̄≥101) = 1-CDF(z) =     __________
x̄ = 103   z=______   P(x̄≥103) = 1-CDF(z) =     __________

   Probability that a sample's mean would be this little or smaller:
x̄ =  99   z=______   P(x̄≤101) = CDF(z) =       __________
x̄ =  97   z=______   P(x̄≤103) = CDF(z) =       __________


Sample size n=30 → SEM=(σ/√n)=_________

   Probability that a sample's mean would be this much or greater:
x̄ = 101   z=______   P(x̄≥101) = 1-CDF(z) =      __________  
x̄ = 103   z=______   P(x̄≥103) = 1-CDF(z) =      __________

   Probability that a sample's mean would be this little or smaller:
x̄ =  99   z=______   P(x̄≤101) = CDF(z) =      __________
x̄ =  97   z=______   P(x̄≤103) = CDF(z) =      __________


Sample size n=100 → SEM=(σ/√n)=_________

   Probability that a sample's mean would be this much or greater:
x̄ = 101   z=______   P(x̄≥101) = 1-CDF(z) =     __________
x̄ = 103   z=______   P(x̄≥103) = 1-CDF(z) =     __________

   Probability that a sample's mean would be this little or smaller:
x̄ =  99   z=______   P(x̄≤101) = CDF(z) =      __________
x̄ =  97   z=______   P(x̄≤103) = CDF(z) =      __________


As n gets larger (i.e. larger sample size), the SEM gets _________ and
 sample means x̄ tend to be ___________ to the population mean μ.


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Typical kind of questions:

A population with mean μ=89.5 and SD σ=12.8

Sample size n = 10
Standard deviation of the sampling distribution of the mean: SEM = σ/√n =______

 A sample mean x̄ = 85   → z=________
 How likely is a sample mean x̄ ≤ 85    ________

 A sample mean x̄ = 95   → z=________
 How likely is a sample mean x̄ ≥ 95    ________


Sample size n = 30
Standard deviation of the sampling distribution of the mean: SEM = σ/√n =______

 A sample mean x̄ = 85   → z=________
 How likely is a sample mean x̄ ≤ 85    ________

 A sample mean x̄ = 95   → z=________
 How likely is a sample mean x̄ ≥ 95    ________