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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 dont know the population standard deviation σ, we obviously cant use the formula Confidence Intervals Because weve changed our formula (by using s instead of σ ), we cant use the normal distribution any more Instead of the normal distribution, we use the Students 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 Students t distribution Properties of the t-distribution Several properties are familiar about the Students 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 Students 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 Students 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 Students 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 Students 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 Students t curve gets close to, but never reaches, 0 Confidence Intervals So whats different?...

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