Stats: Confidence Intervals
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A point estimate is
- the statistic (single value), computed from sample information, which is used to
- estimate the population parameter
A point estimate of a population parameter is a single value of a statistic. For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P. Interval estimate.
A confidence interval estimate is
A confidence interval estimate is a range of values constructed from sample data so that the population parameter is likely to occur within that range at a specified probability
In statistics, a confidence interval (CI) is a type of interval estimate of a population parameter. It is an observed interval (i.e. it is calculated from the observations), in principle different from sample to sample, that frequently includes the parameter of interest if the experiment is repeated.
Confidence intervals consist of a range of values (interval) that act as good estimates of the unknown population parameter; however, in infrequent cases, none of these values may cover the value of the parameter.
The specified probability in a confidence interval is called the
level of confidence
It is expressed as a percentage and represents how often the true percentage of the population who would pick an answer lies within the confidence interval. The 95% confidence level means you can be 95%certain; the 99% confidence level means you can be 99% certain.
Types of estimates: Can you estimate the population mean if you don't know the standard deviation?
If the population standard deviation is unknown....we substitute the sample standard deviation (s) for the population standard deviation (σ)
The probability that the confidence interval will contain the population mean m in repeated samples is denoted by
1 - a also known as the "confidence coefficient"
A confidence coefficient, or confidence level, is a measure of the accuracy and repeatability of a statistical test.
(1 – a) x 100%
1 – a
What kind of curve do you use as a model for the sampling distribution of the sample mean?
The normal curve
•Exactly, if the population is normal
- •Approximately, by the Central Limit
- Theorem for large samples of any distribution
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