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# Comparing Two Means

Can a waitress earn higher tips simply by giving her name when she greets her customers? How can she design an experiment to investigate this? After she collects the data, how can she decide whether the results are statistically significant enough to convince her that telling customers her name really helps? And if she decides that giving her name helps, how can she estimate how much higher her tips will be, on average, when telling customers her name? In this topic, you will learn a statistical inference procedure for answering such questions.

## Overview

In the previous topic, you studied the application of inference techniques to the comparison of two proportions. In this topic, you will examine the case of comparing two sample means. These inference procedures will again be based on the t-distribution. You will explore the effects of factors such as sample size and sample variability on these procedures. As you progress through this topic, you will find that the reasoning behind and interpretation of the procedures remain the same, and that an initial examination of the data, graphical and numerical, prior to applying formal inference procedures is, as always, important. You will again see that the method used to collect the data determines the scope of conclusions that can be drawn.

## Preliminaries

1. If one commuting route has a sample mean travel time of 32 minutes and another route has a sample mean commuting time of 28 minutes, what else would you ...

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