Inference for Means
CHAPTER OUTLINE
Introduction
We began our study of data analysis in Chapter 1 by learning graphical and numerical tools for describing the distribution of a single variable and for comparing several distributions. Our study of the practice of statistical inference begins in the same way, with inference about a single distribution and comparison of two distributions. These methods allow us to address questions such as these:
- Customer surveys provide companies feedback on the satisfaction with, and use of, current products or services. A recent survey commissioned by Samsung and O2 reports smartphone users in the United Kingdom spend an average of 119 minutes a day on their smartphones. Do you think smartphone users in the United States spend more or less time on their phones? How would you go about answering this question?
- A smart shopping cart is a cart that includes a scanner, which reports the total price of the goods in the cart. Would you like to see this technology at your local grocery store? Do you think it would influence your spending? If so, do you think you’d typically spend more or less? Grocery store chains, such as Safeway and Kroger, are interested in understanding these preferences and spending effects. How might you test to see if a smart cart increases spending?
- Do you expect to be treated rudely by salespeople of high-end retail such as Gucci and Burberry? If yes, why? There are some who argue that this rudeness adds value to the goods being sold. Do you agree? If so, would rudeness add value even at a mass market store, such as Gap or Target? We’ll consider a pair of experiments that try to answer these questions.
Two important aspects of any distribution are its center and spread. If the distribution is Normal, we describe its center by the mean μ and its spread by the standard deviation σ. In this chapter, we will consider confidence intervals and significance tests for inference about a population mean μ and the difference between population means μ1−μ2. Chapter 6 emphasized the reasoning of significance tests and confidence intervals; now we emphasize statistical practice and no longer assume that population standard deviations are known. As a result, we replace the standard Normal sampling distribution with a new family of t distributions. The t procedures for inference about means are among the most commonly used statistical methods in business and economics.