10/5/10 Week 7
Population the “big group” we are interested in
Sample same subset of that population
Parameter a population value of interest, of the unknown (one single value)
Ex. The population of all registered voters who will vote for democrat this election or the
mean SAT score of all PSU freshmen.
Statistic value from sample to estimate a parameter
Ex. The sample proportion or the sample mean, mean of everyone’s height
The sample statistic are also called “point estimates”
For us we are going to concentrate on two statistics:
1. Sample proportion – symbol read pi hat
2. Sample mean symbol read xbar
If we roll a sixsided die what is the mean outcome and standard deviation?
Mean = 3.5 Standard Deviation= 1.7
What if we had everyone roll the die twice and get average of their two rolls?
Mean of the averages would be? Mean= 3.5 Standard deviation s/n▯ = 1.▯/2
Now you roll die 100 times and record mean of your 100 rolls.
What do you think the mean of all these averages would be?
Mean= 3.5 Standard Deviation=s/1 ▯ 00
1 roll average from 1 to 6 straight line 2 rolls average from 1 to 6 peak at 3.5 100 roll average from 1 to 6 bell shape
Central Limit Theorem: if the sample size is large enough then the sample mean will fallow an
approximate normal distribution with a mean of M and standard deviation of s/n ▯
M Read “mu” is population mean
s Read “sigma” is population standard deviation
Large Enough is when n is at least 30 OR if we know the population distribution is normal then by
rule the sample mean