Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 19

Confidence Intervals: Means

How many M&M candies do college students tend to grab? For how long did an “average” student at your school sleep last night? How much weight does a typical college student carry in his or her backpack? Although these questions concern different contexts, they nevertheless sound quite similar. In this topic, you will learn how to construct a confidence interval to address these and other questions.

Overview

In Topic 16, you explored confidence intervals for a population proportion. In this topic, you will turn from binary categorical variables to quantitative variables, so now the population mean is the parameter of interest. You will investigate and apply confidence interval procedures for estimating a population mean. Although some of the procedure's details are different, and you will work with a new probability model called a t-distribution, you will find that the reasoning, structure, and interpretation of a confidence interval remain unchanged.

Preliminaries

1. Guess the average amount of sleep that a student in your class got last night. Then make guesses for the least and most hours of sleep that a student in your class got last night. (Activity 19-4)

   

2. Mark on the following scale an interval that you believe with 90% confidence to include the mean amount of sleep (in hours) that students at your school got last night. (Activity 19-4)