Transcript day4 - University of South Carolina

STAT 110 - Section 5
Lecture 4
Professor Hao Wang
University of South Carolina
Spring 2012
Last time
Bad sample:
Convenience and voluntary sample
Good sample:
Simple random sample (SRS)
This time
• How to get a simple random sample (SRS)
Random Digits
table of random digits – a long string of the digits
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
with the following two
properties:
1. Each entry in the table is equally likely to
be any of the 10 digits 0 through 9.
2. The entries are independent of each
other. That is, knowledge of one part of
the table gives no information about any
other part.
Random Digits
• Table A on pages 550-551
• The digits appear in groups of 5 to make the
table easier to read.
• The groups and rows have no meaning.
• So, how do you use the table?
• Digits can be read across a row, down a column,
or in any other order.
• Standard practice is to read across the row.
Random Digits Example
A firm wants to understand the attitudes of its
minority managers toward its system for assessing
management performance. Use Table A at line 102
to choose 6 minority managers to be interviewed.
01-Agarwal
02-Alfonseca
03-Baxter
04-Bowman
05-Cortez
06-Cross
07-Dewald
08-Fleming
09-Gates
10-Goel
11-Gomez
12-Hernandez
13-Huang
14-Kim
15-Liao
16-Mourning
17-Peters
18-Puri
19-Rodriguez
20-Shen
21-Vega
Random Digits
• Step 1: Label
Assign a numerical label to every individual in
the population (sampling frame). All labels
must have the same number of digits.
• Step 2: Table
Use the random number table to select labels
at random.
Random Digits Example
Let the class be the population.
Let’s take an SRS of size n=2.
There are N=200 on the roll. Everyone
numbers off.
Since all labels must have the same number
of digits, the numbers should be 001 to 200.
Start with line 116 of Table A.
How do we read it? Who is chosen as our
sample?
Problem 3
You are reporting on apartments in Columbia. You
decide to select 3 complexes at random for in-depth
interviews with residents. Use Table A at line 116
(read across the row) to select your sample.
01-Abbott Arms
02-Asbury Arms
03-Ashland
04-Bent Tree
05-Briargate
06-Brook Pines
07-Cedarwood
08-Claire Tower
09-Colony East
10-Cornell Arms
11-Fairways
12-Fox Run
13-Green Oaks
14-Hunter’s Green
15-Keswick
16-Landmark
17-Paces Run
18-Ravenwood
19-Riverview
20-Stone Ridge
21-Whaley’s Mill
Problem 3
The third complex chosen is:
A - 03
B - 10
C - 14
D - 45
E - 92
Comparing sampling methods
You will be given a sheet of 100 rectangular
shapes. Leave it face down until told to look.
When told to, flip it over for 5 seconds and
make a guess at the average size of the
rectangles on the sheet. Then flip it back over.
Write your guess down.
Choosing a non-random sample
Now, look at the sheet and pick five rectangles
that you think are most representative. Take
their average by adding up the total number of
squares and dividing by 5.
Write that value down.
Randomly choosing a convenience sample
This time we need to use the random number
table.
Use the row corresponding to the day your
birthday falls on (if the 26th – 30th, wrap back
around to the top of the page). So if your
birthday is the 1st use row 101, if it’s the 24th
use row 124, and if it’s the 26th you wrap back
around and use 101 too.
Start a number of digits in equal to the month
you were born in.
Randomly choosing a convenience sample (pt. 2)
Now choose the first number from 00 to 99 and
take that rectangle (remember 00=100) and
the four closest to it.
Add up their sizes and divide by 5.
Using a simple random sample
Take the next five numbers from 00 to 99 as
your simple random sample of size five. Add
up their sizes and divide by 5.
What range was your guess in?
A – 3.9 or less
B – 4.0 to 5.6
C – 5.7 to 9.1
D – 9.2 to 10.9
E – 11.0 or higher
Choose 5 you think are representative:
A – 3.9 or less
B – 4.0 to 5.6
C – 5.7 to 9.1
D – 9.2 to 10.9
E – 11.0 or higher
Take a convenience sample:
A – 3.9 or less
B – 4.0 to 5.6
C – 5.7 to 9.1
D – 9.2 to 10.9
E – 11.0 or higher
Take a SRS:
A – 3.9 or less
B – 4.0 to 5.6
C – 5.7 to 9.1
D – 9.2 to 10.9
E – 11.0 or higher
True or False
In a table of random digits:
Each pair of digits has chance 1/100 of being 33
A.True B. False
True or False
In a table of random digits:
There are exactly four 4s in each row of 40 digits.
A.True B. False
True or False
In a table of random digits:
The digits 99999 can never appear as a group,
because this pattern is not random.
A.True B. False
True or False
In a table of random digits:
The digits 34965 are more random than 24242.
A. True B. False