Using R for Introductory Statistics : John Verzani

Chapter 7Confidence intervalsIn this chapter we use probability models to make statistical inferences about the parentdistribution of a sample. A motivating example is the way in which a public-opinion pollis used to make inferences about the unknown opinions of a population.7.1 Confidence interval ideas■ Example 7.1: How old is the universe? The age .universe (UsingR) data set containsestimates for the age of the universe, dating back to some early estimates based on theage of the earth. As of 2003, the best estimate for the age of the universe is 13.7 billionyears old, as computed by the Wilkinson microwave anisotropy probe(http://map.gsfc.nasa.gov/). This is reported to have a margin of error of 1% with 95%confidence. That is, the age is estimated to be in the interval (13.56, 13.84) with highprobability. Figure 7.1 shows other such intervals given by various people over time.Most, but not all, of the modern estimates contain the value of 13.7 billion years. Thisdoes not mean any of the estimates were calculated incorrectly. There is no guarantee,only a high probability, that a confidence interval will always contain the unknownparameter.7.1.1 Finding confidence intervals using simulationTo explore the main concepts of a confidence interval, let’s consider the example of asimple survey. We’ll assume the following scenario. A population exists of 10,000people; each has a strong opinion for or against some proposition. We