Solutions to Cumulative Review Problems
a, c, and d are quantitative.
- a, d, and e are continuous; b and c are discrete. Note that (d) could be considered discrete if what we
meant by “number of square miles” was the integer number of square miles. - Statistics is the science of data. Its two main divisions are data analysis and inference . Data
analysis (EDA) utilizes graphical and analytical methods to try to see what the data “say.” That is,
EDA looks at data in a variety of ways in order to understand them. Inference involves using
information from samples to make statements or predictions about the population from which the
sample was drawn. - A survey, based on a sample from some population, is usually given in order to be able to make
statements or predictions about the population. An experiment, on the other hand, usually has as its
goal studying the differential effects of some treatment on two or more samples, which are often
composed of volunteers. - Statistical inference is based on being able to determine the probability of getting a particular
sample statistic from a population with a hypothesized parameter. For example, we might ask how
likely it is to get 55 heads on 100 flips of a fair coin. If it seems unlikely, we might reject the notion
that the coin we actually flipped is fair. The probabilistic underpinnings of inference can be
understood through the language of random variables. In other words, we need random variables to
bridge the gap between simple data analysis and inference.