STAT202 Study Guide - Final Guide: Confidence Interval, Interval Estimation, Statistical Parameter
STAT: Chapter 4a: Introduction to
Interference
Statistical inference
• Provides methods for drawing conclusions about a population from sample data
• Because a different sample might lead to different conclusions, we can’t be certain that
our conclusions are correct
• Uses the language of probability to saw how trustworthy our conclusions are
• Two most common types of inference:
o Confidence Intervals: for estimating the value of the population parameter
o Test of Significance: to assess the evidence for or against a claim about a
population
Simple Conditions for Inference about a Mean
1) The data must be an SRS from the population
• The z procedures are not correct for samples other than SRS
• Always explore your data before performing an analysis
o There are no outliers – the sample mean is strongly influenced by outliers
o There is no no-response or other practical difficulty
2) The variable we measure has a perfectly normal distribution Nμ, σ
• The shape of the population distribution matters
o In practice, the z procedures are reasonably accurate for any sample of at
least moderate size from a fairly symmetric distribution
o Skewness makes the z procedure untrustworthy unless the sample is large
3) The population standard deviation, σ, must be known\
• Unfortunately, σ is rarely known, so z procedures are rarely useful
• We will introduce procedures when σ is unknown
Uncertainty and Confidence
• A point estimate is a single number
o How much uncertainty is associated with a point of estimate of a population
parameter?
• If you picked different samples from a population, you would probably get different
sample means. Virtually none of them would actually equal the true population mean –
this is sampling variability
• An alternative to reporting a single value for the parameter being estimated is to
calculate and report an entire interval of plausible values – a confidence interval (C.I.)
o A confidence interval is a measure of the degree of reliability of the interval –
tells you how sure you can be
Use of Sampling Distributions
• If the population is Nμ, σ, the sampling distribution is Nμ, σ/√).
• If not Nμ, σ, the sampling distribution is ~ Nμ, σ/√) if n is large enough
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Document Summary
If the population is n(cid:523) , (cid:524), the sampling distribution is n(cid:523) , / (cid:1866)). If not n(cid:523) , (cid:524), the sampling distribution is ~ n(cid:523) , / (cid:1866)) if n is large enough. If you picked different samples from a population, you would probably get different: how much uncertainty is associated with a point of estimate of a population tells you how sure you can be. Use of sampling distributions this is sampling variability: an alternative to reporting a single value for the parameter being estimated is to. Uncertainty and confidence: a point estimate is a single number parameter, we take one random sample of size n, and rely on the known properties of the sampling distribution. A confidence interval (c. i. ) can be expressed as: estimated margin of error (m: all c. i. are symmetric about the parameter, the margin of error is half the size of the entire interval. Case i: c. i. for a normal population mean ( known)
