Transcript Chapter 9: Means and Proportions as Random Variables

Chapter 9: Means and
Proportions as Random Variables
• 9.1 Understanding dissimilarity among
samples
• 9.2 Sampling distributions for sample
proportions
• 9.3 What to expect of sample means
• 9.4 What to expect in other situations:
Central Limit Theorem
• Etc.
Chapter 9 dependencies
Chapter 9
9.1
Dissimilarity
among
samples
Histograms
(Sect. 2.5)
9.2-9.4
Proportions,
sample means,
CLT
Normal
distributions
(Sect. 2.7, 8.6)
9.5
Sampling
Distribution
Standard
deviation
(Sect. 2.7)
9.8
Statistical inference
9.6
Standardized
Statistics
9.7
T distributions
9.1 Understanding dissimilarity
among samples
Suppose we have a population with known
characteristics (as in your lab).
We propose to pick a random sample from this
population.
The science of probability can describe for us
the random behavior of this sample.
9.1 cont’d: “Statistics is
Probability in reverse”
On the other hand, if we have a population with
unknown properties, suppose we select a sample at
random.
In Statistics, we use certain characteristics (statistics) of
the sample to learn about the properties (parameters) of
the population.
Probability: Describe sample behavior from population
characteristics.
Statistics: Infer population behavior from sample
characteristics by applying probability logic in reverse.
Probability Statement:
Statistics Statement:
9.2 An example involving
proportions
Recent studies have shown that about 20% of American
adults fit the medical definition of being obese. A large
medical clinic would like to estimate what percent of its
patients is obese, so it takes a random sample of 100
patients and finds that 18 are obese. Suppose that in truth,
the same percent holds for the patients of the medical clinic
as for the general population, 20%.
(Problem 9.11, page 281)