Topics

1. Discussion of Mini-Project - Percentage of SUV's
2. Introduction to JMP
3. Creating a RANDOM SAMPLE in JMP
4. If you did not complete the CLASS SURVEY last week, please do so during the lab time.

SUV Mini-Project

Sports Utility Vehicles (SUVs) have shown tremendous growth in market share over the last 10 years. For this Mini-project, your group will design and carry out a study to estimate the percentage of vehicles that are SUVs in a large parking lot. For example, you might use the W lot on Wannamaker, The Ocean.

In your groups, design a sampling scheme you can use to estimate the percentage of vehicles that are SUVs. Think about:

• What is the Sampling Frame? Is this the list of vehicles or the list of Parking Spaces? What should you do if this information is not known in advance or could fluctuate over time?

• Would a systematic sample be appropriate? (A systematic sample would involve sampling say every 10th vehicle.) Could vehicle size/parking space size create a systematic bias in how vehicles are parked? Are there restrictions for handicap parking? Compact car spaces?

• In a simple random sample, every vehicle (in your sampling frame) is equally likely to be included in the sample. How would you carry out a simple random sample? Do you need to know the total number of vehicles in the lot to do this? Or the total number of parking places? (Below, we will describe using JMP IN how to generate a random series of random numbers that can be used to create a simple random sample.)

• How do you handle cars parked on the grass/off the pavement? Can this bias results?

• In choosing the number to sample, consider the margin of error that will accompany your sample result. How large a sample do you need if you want your margin of error to be within +/- 5 percentage points? +/- 1 percentage point? +/- .01 percentage points?

• For review: is this an observational study or an experiment? What data are being collected? (categorical, discrete, continuous?) Do you have valid measurements? reliable measurements? How do the 7 Critical Components affect your study design?

• Here is a list of SUVs that you may find useful in defining whether a vehicle is a SUV.

As a group, turn in typed report (1 page MAX) describing your study. In your report, be sure to

1. Explain your sampling method and discuss any problems or biases you encountered using it. What time of day or day of the week did you collect data?

2. Construct an interval from your sample that almost surely covers the true population percentage of SUVs for that lot. Does your interval cover the true population percentage you found when you took the census?

3. Use your experience with taking the census to give one practical difficulty with taking a census. ( Hint: did all the vehicles stay put while you counted? Now aren't you glad you did not have to take a survey to estimate the percentage of grey whales! :-)

4. Discuss the limitations of this survey. Can these results be used to estimate the percentage of DUKE Students that own SUVs? The percentage of SUVs at DUKE? Explain. Does it matter which lot you use - the ocean, the Duke Garden lot, an RT lot, a lot on East Campus, Trent?

INTRODUCTION TO JMP IN

Start up JMP

1. FIND a PC in the lab or on campus that has JMP
2. Go to the START Menu at the bottom left side of the screen
3. Hold the mouse button down and then drag to select
4. Programs ->, then Statistics and Mathematics Programs ->, then select JMP IN
5. The program should start with a blank spread sheet "Untitled 1"

Creating a Random Sample

Using JMP, we will create a random order of the numbers 1 to 500 using the "SHUFFLE" command. If we want to take a 10% sample, then we use all vehicles that have SHUFFLED number less than or equal to 50. Let's see how to do it!

The first step is to create an initial table with 500 rows.

1. Go to the Rows Menu at the top of the JMP IN Menu bar.
2. Select Add Rows...
3. In the pop-up window, enter the number of rows you want to add (500 or whatever you will use as the population size - for lab you might try initially with just 20)
4. Click Add

The second step is to create a variable that provides an index of the population (1 to 500) in Column 1. We can do this using JMP IN's Spreadsheet Calculator.

1. Click in the space at the top of Column 1 (if selected the square region at the top should be black). This selects a column.
2. Go to the Cols (column) Menu at the top Menu bar and select Column Info
3. In the pop-up window, go to the Data Source: field. Click on the down arrow, and then select Formula. Click the OK box.
4. This brings up the Calculator. In the middle scroll box at the top of the calculator, click on Terms . (this allows us to specify a "term" in our formula for defining Column 1. Then in the right menu, select i[row #]. Click Evaluate. You have just evaluated a formula that sets each row in column 1 to be its row number, i.
5. Go to the "Jumping Man" icon at the upper left corner of the "Column 1" calculator window, and select Close.
6. Back in your spreadsheet table, you should now have Column 1 filled in with the values 1 to 500.
7. To rename Column 1 something more meaningful, just highlight the text "Column 1" with the mouse, and then type in the new name, say "Vehicle #".

1. Double click the mouse in the "triangular region" in the upper left corner of the spread sheet with the text "1 Cols". This should bring up a menu to create a new column. (You can alternatively add a column with the Cols Menu.)
2. In the Col Name field, enter a name, say "Sample #".
3. In the Data Source field, select Formula
4. Click on OK to bring up the Calculator.
5. In the Calculator window, go to the middle scroll box, and select Random
6. In the right scroll box window, select Shuffle (you should see ?shuffle in the formula box window at the bottom of the calculator window.
7. Click Evaluate
8. Close the calculator window (go to the "Running Man" menu next to "Sample #", and select Close.)

You should now have a column with the numbers 1 to 500 in random order!

To print your table, go to the File menu and select Print. You can also cut and paste info to other programs or use the Journal under the Edit menu

To use this to create a 20% sample (sample size is then 100), you would sample vehicles that have a sample number less than or equal to 100. We are keeping the lists sorted by vehicles, since it may be easier to go through the vehicles in order 1, 2,... and find out if they are in the sample or not. Going through in order of the sample numbers requires that we first go to vehicle 50, then to vehicle 11, etc, which may be more difficult to implement in our context.

For example, here is output for a table based on 10 vehicles. To take a sample of size 4, we would sample only the vehicles that have a sample number less than or equal to 4; we would sample vehicles 1, 4, 6, and 7. As you sample each vehicle keep a running tally of the number of SUVs.