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**Unformatted text preview: **Chapter 9 Section 2 Confidence Intervals about a Population Mean in Practice where the Population Standard Deviation is Unknown Chapter 9 – Section 2 ● Learning objectives Know the properties of t-distribution Determine t-values Construct and interpret a confidence interval about a population mean 1 2 3 Confidence Intervals ● In Section 1, we assumed that we knew the population standard deviation σ ● Since we did not know the population mean μ , this seems to be unrealistic ● In this section, we construct confidence intervals in the case where we do not know the population standard deviation ● This is much more realistic Confidence Intervals ● If we don’t know the population standard deviation σ, we obviously can’t use the formula Confidence Intervals ● Because we’ve changed our formula (by using s instead of σ ), we can’t use the normal distribution any more ● Instead of the normal distribution, we use the Student’s t-distribution ● This distribution was developed specifically for the situation when σ is not known Confidence Intervals ● Properties of the t-distribution ● Several properties are familiar about the Student’s t distribution ● Properties of the t-distribution ● Several properties are familiar about the Student’s t distribution Just like the normal distribution, it is centered at 0 and symmetric about 0 ● Properties of the t-distribution ● Several properties are familiar about the Student’s t distribution Just like the normal distribution, it is centered at 0 and symmetric about 0 Just like the normal curve, the total area under the Student’s t curve is 1, the area to left of 0 is ½, and the area to the right of 0 is also ½ ● Properties of the t-distribution ● Several properties are familiar about the Student’s t distribution Just like the normal distribution, it is centered at 0 and symmetric about 0 Just like the normal curve, the total area under the Student’s t curve is 1, the area to left of 0 is ½, and the area to the right of 0 is also ½ Just like the normal curve, as t increases, the Student’s t curve gets close to, but never reaches, 0 Confidence Intervals ● So what’s different?...

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