Class 01
Why statistics?
• Someone is interested in learning something about a population of somebodies. Perhaps even interested in comparing two or more populations.
• But, populations are often too large to measure all of the somebodies.
• So, take a random sample of somebodies from the population. Use the measurements
(data) on the sample to draw conclusions about the larger population.
• Use probability calculations to help draw the conclusions.
Example #1
Chapter 7
Derive “point estimates” and “confidence intervals” for:
Population parameter
... based on ...
population mean µ
difference in two population means µ1 − µ2
population variance σ 2
population proportion p
difference in two population proportions p1 − p2
Sample statistic
sample mean x
difference in sample means, x1 − x2
sample variance s2
sample proportion pb
difference in two sample proportions pb1 − pb2
Also, unbiasedness, how sample size affects the width of confidence intervals, and linear
regression estimates.
Example #2
Chapter 8 and 9
Derive “hypothesis testing” procedures for:
Population parameter
... based on ...
population mean µ
difference in two population means µ1 − µ2
population variance σ 2
population proportion p
difference in two population proportions p1 − p2
1
Sample statistic
sample mean x
difference in sample means, x1 − x2
sample variance s2
sample proportion pb
difference in two sample proportions pb1 − pb2
Plus:
• comparing more than two means µ1 , µ2 , ..., µk
• comparing more than two proportions p1 , p2 , ..., pk
• testing in linear regression
• ensuring a “powerful” hypothesis test
What about chapter 6?
• To derive confidence interval formulas and hypothesis testing procedures, we need to
know the probability distributions of each of the relevant sample statistics (shape,
mean, variance, formula, ...)
• A “sampling distribution” is just a special name for a probability distribution of a
sample statistic.
• Chapter 6 just adds more tools to our probability toolbox ... the ones we need to
develop the confidence intervals of Chapter 7 and the hypothesis tests of Chapter 8.
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