The Practice of Statistics, 5th Edition

Starnes, Tabor, Yates, Moore

Bedford Freeman Worth Publishers

CHAPTER 4Designing Studies

4.1

Samples and Surveys

The Practice of Statistics, 5th Edition 2

2. An archaeological dig turns up

large numbers of pottery shards,

broken stone tools, and other

artifacts. Students working on the

project classify each artifact and

assign it a number. The counts in

different categories are important for

understanding the site, so the project

director chooses 25 of the artifacts at

random and checks the students’

work. Identify the population and the

sample.

8. You have probably seen the mall

interviewer, approaching people

passing by with clipboard in hand.

Explain why even a large sample of

mall shoppers would not provide a

trustworthy estimate of the current

unemployment rate.

HW

The population is all the artifacts

discovered at the dig. The sample is

those artifacts (2% of the population)

that are chosen for inspection.

This is a convenience sample. The

sample is likely to overestimate the

unemployment rate because people

without jobs have more time to be at

the mall than those who are

employed.

The Practice of Statistics, 5th Edition 3

10. In June 2008, Parade magazine

posed the following question:

“Should drivers be banned from

using all cell phones?” Readers

were encouraged to vote online at

parade.com. The July 13, 2008

issue of Parade reported the

results: 2407 (85%) said “Yes” and

410 (15%) said “No.”

a) What type of sample did the

Parade survey obtain?

b) Explain why this sampling method

is biased. Is 85% probably higher

or lower than the true percent of

all adults who believe that cell

phone use while driving should be

banned? Why?

HW

a) A voluntary response sample

b) The reported value of 85% is

probably higher than the true

percent because readers who

have been involved in an

accident caused by cell phone

use are more likely to respond to

the poll and say yes.

The Practice of Statistics, 5th Edition 4

12.You are planning a report on

apartment living in a college town .

You decide to select three

apartment complexes at random

for in-depth interviews with

residents.

a) Explain how you would use a line

of Table D to choose an SRS of 3

complexes from the list below.

Explain your method clearly

enough for a classmate to obtain

your results.

b) Use line 117 to select the sample.

Show how you use each of the

digits.

HW

a) Number the 33 complexes from 01 to

33 alphabetically. Go to the random

number table and pick a starting

point. Record two-digit numbers,

skipping any that aren’t between 01

and 33 and any repeated numbers,

until you have 3 unique numbers

between 01 and 33. Use the 3

complexes corresponding to these

numbers.

b) Starting at line 117 we read off the

following numbers: 38 (ignore) 16

(select) 79 (ignore) 85 (ignore) 32

(select) 62 (ignore) 18 (select). We

have selected: Fairington (16),

Waterford Court (32) and Fowler (18).

The Practice of Statistics, 5th Edition 5

Sample Activity – Who wrote the Federalist Papers?

Please open your book to page 218 again, to complete the activity.

The Practice of Statistics, 5th Edition 6

You are on the staff of a member of

Congress who is considering a bill

that would provide government-

sponsored insurance for nursing-

home care. You report that 1128

letters have been received on the

issue, of which 871 oppose the

legislation. “I’m surprised that most of

my constituents oppose the bill. I

thought it would be quite popular,”

says the congresswoman. Are you

convinced that a majority of the voters

oppose the bill? How would you

explain the statistical issue to the

congresswoman?

Explain it to the Congresswoman

Letters to legislators are an example

of a voluntary response sample—the

proportion of letters opposed to the

insurance should not be assumed to

be a fair representation of the

attitudes of the congresswoman’s

constituents. Only those who have

very strong opinions will write in. In

this case, it is likely that the true

proportion of constituents who

oppose the bill is less than 871/1128.

Learning Objectives

After this section, you should be able to:

The Practice of Statistics, 5th Edition 7

IDENTIFY the population and sample in a statistical study.

IDENTIFY voluntary response samples and convenience samples.

EXPLAIN how these sampling methods can lead to bias.

DESCRIBE how to obtain a random sample using slips of paper,

technology, or a table of random digits.

DISTINGUISH a simple random sample from a stratified random

sample or cluster sample. Give the advantages and disadvantages

of each sampling method.

EXPLAIN how undercoverage, nonresponse, question wording, and

other aspects of a sample survey can lead to bias.

Samples and Surveys

The Practice of Statistics, 5th Edition 8

Stratified Random Sample

To get a stratified random sample, start by classifying the population

into groups of similar individuals, called strata.

Then choose a separate SRS in each stratum and combine these

SRSs to form the sample.

The basic idea of sampling is straightforward: take an SRS from the

population and use your sample results to gain information about the

population.

Sometimes there are statistical advantages to using more complex

sampling methods.

The Practice of Statistics, 5th Edition 9

Cluster Sample

To get a cluster sample, start by classifying the population into groups

of individuals that are located near each other, called clusters.

Then choose an SRS of the clusters. All individuals in the chosen

clusters are included in the sample.

Although a stratified random sample can sometimes give more precise

information about a population than an SRS, both sampling methods

are hard to use when populations are large and spread out over a wide

area.

In that situation, we’d prefer a method that selects groups of individuals

that are “near” one another.

The Practice of Statistics, 5th Edition 10

A Good Read

A school librarian wants to know the average number of

pages in all the books in the library. The library has 20,000

books, arranged by type (fiction, biography, history, and so

on) in shelves that hold about 50 books each. You want to

select a random sample of 500 books.

a) Explain how to select a simple random sample of 500

books.

Number the books from 1 to 20,000. Use the

command randInt(1,20000) repeatedly until 500

different numbers between 1 and 20,000 are selected.

Use the books that correspond to these numbers.

The Practice of Statistics, 5th Edition 11

A Good Read

A school librarian wants to know the average number of pages in all the

books in the library. The library has 20,000 books, arranged by type (fiction,

biography, history, and so on) in shelves that hold about 50 books each.

You want to select a random sample of 500 books.

b) Explain how to select a stratified random sample of 500 books. Justify

your choice of strata. Why might the librarian want to choose a stratified

random sample?

Stratify by type because different types of books might be longer (or

shorter) than other types. This will provide a more precise estimate of the

average page length than a simple random sample.

To select the sample, take an appropriately sized SRS of each type of book

and combine the books selected from each type to form the sample.

For example, if there are 1000 biographies (5% of 20,000), select an SRS

of 25 biographies (5% of 500) using the method described in part (a).

The Practice of Statistics, 5th Edition 12

A Good Read

A school librarian wants to know the average number of pages in all the

books in the library. The library has 20,000 books, arranged by type

(fiction, biography, history, and so on) in shelves that hold about 50

books each. You want to select a random sample of 500 books.

c) Explain how to select a cluster sample of 500 books. Justify your

choice of clusters. Why might the librarian want to choose a cluster

sample?

Clusters are formed by grouping books that are located near each

other, making it easier for the librarian.

We can use each shelf of 50 books as a cluster and randomly select 10

shelves to obtain the 500 books for our sample.

Number the shelves from 1 to 400 and choose an SRS of 10 shelves

using the method described in part (a). Then use all the books on the

10 selected shelves as the sample.

The Practice of Statistics, 5th Edition 13

Random Digits

In using Table D repeatedly to choose random samples, you should not

always begin at the same place, such as line 101. Why not?

If you always begin at the same place, then the results would not be

random. You would end up using the same sample in every case.

Section Summary

In this section, we learned how to…

The Practice of Statistics, 5th Edition 14

IDENTIFY the population and sample in a statistical study.

IDENTIFY voluntary response samples and convenience samples.

EXPLAIN how these sampling methods can lead to bias.

DESCRIBE how to obtain a random sample using slips of paper,

technology, or a table of random digits.

DISTINGUISH a simple random sample from a stratified random

sample or cluster sample. Give the advantages and disadvantages of

each sampling method.

EXPLAIN how undercoverage, nonresponse, question wording, and

other aspects of a sample survey can lead to bias.

Samples and Surveys

The Practice of Statistics, 5th Edition 15

PAGE 231

18, 20, 24, 26Homework