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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 Since we did not know the population mean , 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 , we obviously can't use the formula Confidence Intervals Because we've changed our formula (by using s instead of ), 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 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 , and the area to the right of 0 is also 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 , and the area to the right of 0 is also 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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