A science, a quantitative discipline concerned with the methods of collection and analysis of data to facilitate wise decision making in the face of uncertainty.
Elementary units
Persons or objects comprising a population of interest.
Population
All elementary units of a defined group
Census
An exhaustive survey on some characteristic of interest of every elementary unit in a population
A social biologist has established that the heights of adult men in the U.S. are normally distributed with a mean of 68 inches and a standard deviation of 4 inches.
The tallest 10% of adult men are at least how tall? (or put differently, 90% of all men are ____ inches tall or less.)
If X (the mean of a simple random sample) is taken from a large population of X values and if the N population values are normally distributed, the sampling distribution of X is also normally distributed, regardless of sample size, n.
Given a population that is not normally distributed, the Central Limit Theorem (CLT) states that:
If X (the mean of a simple random sample) is taken from a large population of X values and if the N population values are not normally distributed, the sampling distribution of X nevertheless approaches a normal distribution as sample size, n, increases.
Any sampling distribution of X is considered normal provided n 30 and also n < .05 N .
[Large sample assumption] [Large population assumption]
Perhaps the most important theorem in the entire field of statistical inference.
Consider what it says:
As long as we take random samples that are sufficiently large absolutely and fairly small relative to population size, we can consider the distribution of sample means to be a normal curve (and proceed to infer population parameters from sample statistics on that assumption).
We need not know or be concerned with the shape of the underlying population distribution (which is often unknowable given the problems with census taking).
20.
Sampling Distribution of the sample mean (X) The sampling distribution of the sample mean relates to the parent population like this:
21.
Sampling Distribution of the sample mean (X) The sampling distribution of the sample mean relates to the parent population like this for the large population case: Formula 1A Formula 1B When selections of sample elements are statistically independent events ; typically referred to as "the large population case," because n < . 05 N
23.
Sampling Distribution of the sample mean (X) The sampling distribution of the sample mean relates to the parent population like this for the small population case: When selections of sample elements are statistically dependent events ; typically referred to as "the small population case,” because n .05 N Formula 1C Formula 1D
Mercury makes the Laser XRi engine used in speed boats. The company claims the engine delivers an average 220 horsepower and that the standard deviation of power delivered is 15 horsepower.
A potential boat manufacturer tests 100 randomly chosen XRi engines for single tests. If the claim is true, what is the probability that the sample mean will be less than 217 horsepower?
Answer: .0228
26.
Sampling distribution of the sample proportion
The sample proportion is
The population proportion is .
27.
Sampling distribution of the sample proportion
The sample proportion follows a normal distribution per the CLT if large samples are taken from a large population:
If n 5 and if n(1- ) 5
we have a large sample.
28.
Sampling Distribution of the sample proportion How the sampling distribution of the sample proportion (P) relates to the parent population:
29.
Sampling Distribution of the sample proportion How the sampling distribution of the sample proportion (P) relates to the parent population large population case : When selections of sample elements are statistically independent events ; typically referred to as "the large population case,” because n < .05 N Formula 1E Formula 1F
30.
Sampling Distribution of the sample proportion How the sampling distribution of the sample proportion (P) relates to the parent population small population case : When selections of sample elements are statistically dependent events ; typically referred to as "the small population case,” because n .05 N Formula 1G Formula 1H
Honda claims that 20% of all prospective buyers of minivans of any brand will be interested in their new 2005 Odyssey people mover.
You survey 200 randomly selected prospective buyers of minivans. You have them watch a Honda-produced promotional video on the new Odyssey and find that 33 of the prospective buyers express interest. Do you believe Honda’s claim based upon statistical analysis?
Answer: The probability of getting the sample result we obtained (or something more extreme) if their claim is true is .108
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