Confidence Intervals

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Overview

  1. 8.1 Interval for the Population Mean
  2. 8.2 Interval for the Population Mean
  3. 8.3 Interval for the Population Proportion
  4. 8.4 Confidence Intervals for the Population Variance and Standard Deviation
  5. Chapter 8 Formulas and Vocabulary
  6. Chapter 8 Review Exercises
  7. Chapter 8 Quiz

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image Motor Vehicle Fuel Efficiency

In these times of rising gasoline prices, we need to be aware of the fuel efficiency of our motor vehicles. The Chapter 8 Case Study, Fuel Efficiency, explores a data set containing 13 different measurements on a population of 1141 vehicle models for model year 2014.1

  • In Section 8.1, we construct and interpret a confidence interval for the population mean City MPG, which is the number of miles a vehicle can travel in city conditions on one gallon of gas, using a large sample. Later, we construct a confidence interval for the population mean Highway MPG, using a small sample and a normal probability plot.
  • Also in Section 8.1, we take many samples of vehicles and construct many confidence intervals for the population mean City MPG, illustrating that it is the confidence intervals that are random, and not the population mean, which is constant.
  • Later in Section 8.1, we calculate and interpret the margin of error for the population mean city gas mileage, and then learn two different ways to reduce this margin of error.
  • In the Section 8.2 exercises, we work with the large data set, Fuel Efficiency, to examine confidence intervals for the population mean amount of carbon dioxide generated by motor vehicles in city driving.
  • Finally, in the Section 8.3 exercises, we again work with the large data set to examine confidence intervals for the population proportions of compact cars and midsize cars.

THE BIG PICTURE

Where we are coming from and where we are headed …

  • We stand on the threshold of the two most important statistical inference methods: confidence intervals and hypothesis testing. From descriptive statistics in Chapters 1-4 through probability and probability distributions in Chapters 5 and 6 and sampling distributions in Chapter 7, everything that we have studied thus far has been in preparation for this moment.
  • Here in Chapter 8, we learn about confidence interval estimation, where we can infer with a certain level of confidence that our target parameter lies within a particular interval.
  • Every chapter from here to the end of the book will uncover a new and different topic in statistical inference. In Chapter 9, “Hypothesis Testing,” we will learn about the most prevalent method of statistical inference.