Stats 309 12-1

Stats 309 12-1 - 12.1 Inference about a Population Mean...

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Unformatted text preview: 12.1 Inference about a Population Mean when σ is unknown • Previously, we were working under the assumption that the population standard deviation, σ, was known. Or, if we didn’t know what σ was, if we took a large enough sample (n>30), we could then use the sample standard deviation, s , to approximate σ. • However, what if we have a more realistic scenario where we don’t know the population standard deviation and we have a small sample size? It makes sense that if we don’t know µ, then we don’t know σ for the same reasons (population too large to deal with, etc.) And sometimes, we can only take a small sample (human experiments, etc.). Then, we are unable to use the Z test statistic because the CLT no longer applies. • In this case, we use a student t test statistic. • The t distribution is close to normal shape. However, it takes into account the ‘instability’ of using sample standard deviation, s , in place of population standard deviation, σ. • The t distribution has a lot of similar properties to the Z distribution: It is mound shaped....
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Stats 309 12-1 - 12.1 Inference about a Population Mean...

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