STA 261 Chapter Notes - Chapter 6-7: Central Limit Theorem, Sampling Distribution, Point Estimation
26 Jun 2018
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Module 6 - Sampling Distributions
● Three different distributions
1. The population distribution
a. Almost never observed
b. We learn all we can about the population distribution from sample
distributions
2. The sample distribution (aka the data distribution)
a. Consists of the sample data you actually observe and analyze
b. Should rough resemble the population distribution
3. The sampling distribution
a. Describes the long-run behavior of the statistic
b. Specifies probabilities for all possible values of the statistic for a sample
of a given size
● The sampling distribution of the sample proportion will be approximately normal as long
as np and n(1-p) are both at least 15
○ Np > 15 (or equal to)
○ n(1-p) > 15 (or equal to)
○ As long as the sample size is large enough it doesn’t matter what shape the
population distribution is
● Central limit theorem assumptions and conditions for the sampling distribution
○ Randomization condition: the data values must be sample randomly or obtained
through a randomized experiment
○ Independence assumption: the sample values must be mutually independent
○ 10% condition: The sample size, n, is no more than 10% of the population
○ Sample size assumption: the sample size, n, has to be large enough to expect at
least 15 successes and 15 failures
● Mu = population mean
● Standard deviation of mu = standard deviation / sq. rt. Of n
Module 7 - Estimating Parameters (one-proportion z-intervals and one-mean
t-intervals) and Statistical Inference: Confidence Intervals
● A parameter describes a population
○ Mu = population mean
○ P = population proportion
○ Curly o = population stan. Dev.
● A statistic describes a sample
○ X bar = sample mean
○ P hat = sample proportion
○ S = sample stan. Dev.
● A point estimate is a single number that is out best guess for the parameter
● Point estimate = sample / number
○ Ex: out of 1832 married adults, 403 met their spouse online. 403/1832 = 0.2199
Document Summary
The sampling distribution of the sample proportion will be approximately normal as long as np and n(1-p) are both at least 15. As long as the sample size is large enough it doesn"t matter what shape the population distribution is. Central limit theorem assumptions and conditions for the sampling distribution. Randomization condition: the data values must be sample randomly or obtained through a randomized experiment. Independence assumption: the sample values must be mutually independent. 10% condition: the sample size, n, is no more than 10% of the population. Sample size assumption: the sample size, n, has to be large enough to expect at least 15 successes and 15 failures. Standard deviation of mu = standard deviation / sq. rt. Module 7 - estimating parameters (one-proportion z-intervals and one-mean t-intervals) and statistical inference: confidence intervals. A point estimate is a single number that is out best guess for the parameter. Ex: out of 1832 married adults, 403 met their spouse online.
