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Chapter6.1

# Chapter6.1 - Chapter 6 Introduction to Inference This...

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Chapter 6: Introduction to Inference This chapter concerns inference procedures for the population average. You will learn about confidence intervals and significance tests to learn about a population average μ . The world uses both of these methods and you need to know both also. 6.1 Estimating with Confidence If the entire population of SAT scores has mean μ and standard deviation σ , then in repeated samples of size 500 the sample mean x has a N( μ , 500 σ ) distribution. Let us suppose that we know that the standard deviation σ of SATM scores in California population is 100 = σ . In repeated sampling the sample mean x follows the normal distribution centered at the unknown population mean μ and having standard deviation 5 . 4 500 100 = = x σ The 68-95-99.7 rule says that the probability is about 0.95 that x will be within 9 points ( σ × 2 ) of the population mean score μ .

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We say that we are 95% confident that the unknown mean score for a California seniors lies between 452 9 461 9 = - = - x and 470 9 461 9 = + = + x . Figure 6.2 x =461 lies within 9 ± of μ in 95% of all samples, so μ also lies within 9 ± of x in samples from more than 250,000 high school seniors in California.
Confidence intervals We will use C to stand for the confidence level in decimal form. For example, a 95% confidence level corresponds to C =0.95. Confidence Interval A level C confidence interval for a parameter is an interval computed from sample data by a method that has probability C of producing an

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