PSYC 202 Chapter Notes - Chapter 7: Normal Distribution, Sampling Distribution, Confidence Interval
15 Jun 2018
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WEEK 7 VIDEO NOTES
Never know the true population mean
Standardized sampling distributions
- To standardize something, scale away the difference in the mean and standard error
o To get rid of Mean –
▪ Subtract it from the distribution
o To get rid of Standard error
▪ Divide both distributions by their respective standard errors
- Standardizing something means that they will have they same mean, standard error and
shape
- Using equations
o X bar = mean of sample
o
o µ = true population mean
o σ x
̄ = standard error
o we know what xbar is but we don’t know what the true population mean is.
Sometimes we don’t know what the standard error is
▪ if it is known = standard normal distribution – good for large sample sizes
not small
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•
o Circles denote information that is coming from the sample
specifically
▪ Xbar= mean of sample
▪ N = number of observations in sample
o Assume true sigma is known and can be estimated from the
sample
▪ If assuming having to estimate the standard error from the sample rather
than being a fixed quantity that is known ahead of time then you end up
with a T distribution as the standardized sampling distribution
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o Xbar comes from sample
Document Summary
Standardizing something means that they will have they same mean, standard error and shape. Using equations: x bar = mean of sample, = true population mean, x = standard error, we know what xbar is but we don"t know what the true population mean is. T-critical values the tscore value at which the green line occurs on the upper and lower sides: The t indicates that it is on the t-score axis. 0. 05 indicates the amount of probability that is being considered for rare events. Df= degrees of freedom (2) indicates how many tails that is going to be in (one or two sides: in confidence intervals it is given by: df=n-1. Confidence intervals expression that represents the probability density that is found between the extreme lines. S over square root n can be abbreviated as a standard error represents the standard error for that sampling distribution. Then subtract xbar from all sides as well.
