Mathematical Statistics with Resampling and R

7

CLASSICAL INFERENCE: CONFIDENCE INTERVALS

In 2010, according to an AP-Gfk Poll conducted on October 13–18, 59% of 846 likely voters responded that they felt things in this country were heading in the wrong direction (http://www.ap-gfkpoll.com/poll_archive.html). We learned in Chapter 6 that = 0.59 is an unbiased point estimate of the true proportion p of those who think the country is headed in the wrong direction, but we do not have any indication of how far off is from the true p. In Chapter 5, we used bootstrap percentile confidence intervals to give a range of plausible values for a parameter. In this chapter, we learn some other ways to obtain confidence intervals.

7.1 CONFIDENCE INTERVALS FOR MEANS

We begin with confidence intervals for a mean, or a difference in means. These are important in their own right and are instructive for other situations.

7.1.1 Confidence Intervals for a Mean, σ Known

Example 7.1 The Centers for Disease Control maintains growth charts for infants and children (http://www.cdc.gov/growthcharts/zscore.htm). For 13-year-old girls, the mean weight is 101 pounds with a standard deviation of 24.6 pounds. We assume that weights are normally distributed. The public health officials in Sodor are interested in the weights of the teens in their town: they ...