Objective Introduction Examples
The Confidence Interval on module targets the following cognitive tasks:
| Task Skills | Concepts | |
|---|---|---|
| CI_mu-1: | Understand the form of a confidence interval on |
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| CI_mu-2: | Compute a large-sample CI on |
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| CI_mu-3: | Compute a small-sample CI on |
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| CI_mu-4: | Compute a CI on |
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| CI_mu-5: | Compute a CI on |
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| CI_mu-6: | Interpret the CI on |
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| CI_mu-7: | Identify the plausible values of |
Understand which values of |
| CI_mu-8: | Understand the family of t-distributions | |
| CI_mu-9: | Understand the properties of the t-distribution | |
| CI_mu-10: | Understand the relationship between the t and standard normal distributions | |
| CI_mu-11: | Determine the number of degrees of freedom for computing a CI | Understand the concept of degrees of freedom |
| CI_mu-12: | Understand error tolerance | |
| CI_mu-13: | Determine the minimum sample size satisfying an error tolerance | Understand minimum sample size |
The sample mean is a point estimate of the population mean µ. This estimate is based on a single sample and another random sample from the same population would almost assuredly result in a different point estimate. We need to know how much these point estimates vary in repeated sampling from the population in order to assess the efficacy of our estimate.
The interval estimate of µ includes a measure of the variability of the point estimate as encapsulated in the error term. It is computed as the sample mean ± t x se, where t is the 1 - (alpha/2) quantile of the t distribution with n - 1 degrees of freedom and se (the standard error) is s/sqrt(n).
Example #1 uses data from an Australian school to set confidence intervals on the perceived width of a classroom in meters.
Self-test