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# Chapter_14 - Chapter 14 Introduction to Inference BPS 5th...

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BPS - 5th Ed. Chapter 14 1 Chapter 14 Introduction to Inference

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BPS - 5th Ed. Chapter 14 2 Provides methods for drawing conclusions about a population from sample data Confidence Intervals What is the population mean? Tests of Significance Is the population mean larger than 66.5? Statistical Inference
BPS - 5th Ed. Chapter 14 3 1. SRS from the population of interest 2. Variable has a Normal distribution N ( μ , σ ) in the population 3. Although the value of is unknown, the value of the population standard deviation is known Inference about a Mean Simple Conditions

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BPS - 5th Ed. Chapter 14 4 A level C confidence interval has two parts 1. An interval calculated from the data, usually of the form: estimate ± margin of error 2. The confidence level C , which is the probability that the interval will capture the true parameter value in repeated samples; that is, C is the success rate for the method. Confidence Interval
BPS - 5th Ed. Chapter 14 5 Case Study NAEP Quantitative Scores (National Assessment of Educational Progress) Rivera-Batiz, F. L., “Quantitative literacy and the likelihood of employment among young adults,” Journal of Human Resources , 27 (1992), pp. 313-328. What is the average score for all young adult males?

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BPS - 5th Ed. Chapter 14 6 Case Study NAEP Quantitative Scores The NAEP survey includes a short test of quantitative skills, covering mainly basic arithmetic and the ability to apply it to realistic problems. Scores on the test range from 0 to 500, with higher scores indicating greater numerical abilities. It is known that NAEP scores have standard deviation σ = 60 .
BPS - 5th Ed. Chapter 14 7 Case Study NAEP Quantitative Scores In a recent year, 840 men 21 to 25 years of age were in the NAEP sample. Their mean quantitative score was 272 . On the basis of this sample, estimate the mean score μ in the population of all 9.5 million young men of these ages.

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BPS - 5th Ed. Chapter 14 8 Case Study NAEP Quantitative Scores 1. To estimate the unknown population mean μ , use the sample mean = 272. 2. The law of large numbers suggests that will be close to , but there will be some error in the estimate. 3. The sampling distribution of has the Normal distribution with mean and standard deviation x x x σ n = 60 840 2 . 1
BPS - 5th Ed. Chapter 14 9 Case Study NAEP Quantitative Scores

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BPS - 5th Ed. Chapter 14 10 Case Study NAEP Quantitative Scores 1. The 68-95-99.7 rule indicates that and μ are within two standard deviations (4.2) of each other in about 95% of all samples. x 267.8 = 4.2 272 = 4.2 - - x 276.2 = 4.2 + 272 = 4.2 + x
Chapter 14 11 Case Study NAEP Quantitative Scores So, if we estimate that μ lies within 4.2 of , we’ll be right about 95% of the time. x

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Chapter_14 - Chapter 14 Introduction to Inference BPS 5th...

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