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Chapter 6

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Florida State University

Political Science

POS 3713

William Berry

Spring

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6.3.1 The Normal Distribution
Often called a “bell curve”
Special properties of the Normal Distribution
1. It is symmetrical about the mean, such that the mode, media, and mean are the same
2. The normal distribution has a predictable area under the curve within speciﬁed distances of the mean (68-95-99 rule)
1 standard deviation in each direction = 68% of the area under the curve
2 (speciﬁcally 1.96) standard deviations in each direction = 95% of the area under the curve
3 standard deviations in each direction = more than 99% of the total area under the curve
Frequency distribution: the distribution of actual scores in a sample (represents the frequency of each value of a particular
variable)
Questions we can answer using the normal distribution
What can we say about a sample?
Calculate the mean
Add up all of the scores and divide by the total number
Calculation: Ybar=(Sigma^nsub”i”=1Ysub”i”)/n
Calculate the standard deviation
SsubY=radical(Sigma^nsub”i”=1Ysub”i”(Ysub”i”-Ybar)^2)/(n-1)
Sigma(Ysub”i”-Ybar)^2 means: for each observation, we subtract its value from the mean, then square
that diﬀerence, then add up all deviations from the mean
Sampling distribution: a hypothetical distribution of sample means
The mean of the sampling distribution would be equal to the true population mean
The standard deviation of the sampling distribution is:
ThetasubYbar =ssubY/radical”n”
“n” = sample size
Standard error of the mean (“standard error”): the standard deviation of the sampling distribution of
sample means; is equal to the sample standard deviation divided by the square root on the sample size
ThetasubY = standard deviation/square root of all outcomes
Conﬁdence interval: the conﬁdence a survey has about the likely location of the population mean
1st: choose a degree of conﬁdence (usually 95% or 2 standard deviations)
Ybar plus/minus 2 x thetasubYbar
Mean plus/minus (2 x standard error)

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