MA/CS 109 The Art and Science of Quantitative Reasoning Estimation and Confidence: Opinion Polls

As we have noted, statistics is the science of learning from data. One important aspect of such learning is statistical inference, wherein we attempt to draw inferences about characteristics of a population based on a sample from that population. Statistical inference problems may take many forms. For the second week of our statistics module in this class, we will focus on the problem of inferring the value of a single numerical summary of the population. Such inferences should have two components: (a) an estimate of the numerical value about which we seek to learn, and (b) a precise statement quantifying our level of confidence (or, conversely, uncertainty) in that estimate. Although we could conceive of many numerical summaries of a population, commonly people are interested in quantities like averages, proportions, quantiles, etc. That is, in the same types of quantities we use in descriptive statistics to summarize a dataset. Rather than trying to cover a broad range of such summaries in a short period of time, we will instead examine just one summary, but in significant depth and detail. We will concentrate on the estimation of proportions, and we will do so specifically within the context of opinion polls. However, the basic paradigm that we unveil and explore is representative of a much larger class of problems.