Statistical Sciences 2244A/B Chapter Notes - Chapter 13: Estimation Theory, Central Limit Theorem, Bias Of An Estimator
22 May 2018
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Stats 2244
Chapter 13
CHAPTER 13.1
Parameters and Statistics
- Parameter: # that describes the population (a parameter is not known, bc we cant examine the
entire population)
- Statistic: # that can be computed from the sample data without making use of any unknown
parameters
- We use statistics to estimate an unknown parameter
- note: statistics come from samples and parameters come from populations
- FOR QUANTITATIVE DATA:
o we write μ for the mean of a population
▪ this is a fixed parameter that is unknown when we use a sample for inference
o The mean of the sample is the familiar , the average of the observations in the sample
▪ This is a statistic that would almost certainly take a different value if we chose
another sample from the same population
o The sample mean from a sample or an experiment is an estimate of the mean μ of the
underlying population.
- FOR QUALITATIVE DATA:
o we use the notation p to indicate the population proportion of individuals of a given
type, a parameter often of unknown value.
o The sample proportion, , is the proportion of individuals of a given type in a sample or
an experiment.
▪ It is a statistic that would almost certainly take a different value if we chose
another sample from the same population.
o The sample proportion is an estimate of the population proportion p.
VIDEO: parameters and statistics:
- Parameter: a # describing a characteristics of the population (usually unknown)
o Examples:
- Statistics: a number, computed from sample data, estimating an unknown parameter
o Examples:
- Very important that we determine whether a mean is a statistic or a parameter and that you
determine whether a percentage is a statistic or a parameter
- Examples:
find more resources at oneclass.com
find more resources at oneclass.com
