Minitab Instructions for Coins Project

This document may change. It would be best to refer to it online rather than printing it out.

Preparing the Data

Loading the Data

The data is on the U: drive in a worksheet.

  1. Choose File / Open Worksheet
  2. Navigate to the U: drive, then the 01 folder, then coins.
  3. Choose the file coins.mtw (the extension may be hidden)
  4. Click OK

Setting the Value Order

By default, Minitab places data in categorical variables in alphabetical order. That means that the order of the coins in the output will be dime, nickel, penny, and quarter. It would be more appropriate to have them in order by their worth: penny, nickel, dime, and quarter.

  1. Left click the mouse any cell in the coin column so the cell is selected
  2. Right click the mouse and choose Column / Value Order
  3. Choose User-specified order
  4. Change the order so it is penny, nickel, dime, quarter
  5. Click OK

Nothing will happen to the data after you set the value order. This only affects the output.

Separating the Data by Coin Type

For some of the reports and graphs we are asked to generate, the data is fine as it is with categorical variables for coin and mint and a quantitative variable for weight. However, some of the graphs and analysis will require that the data for each type of coin be in their own column. That is, we need a column with the weights of all the pennies in it, one with the weights of all the nickels, one for the dimes, and one for the quarters.

Luckily, we don't have to copy and past the data to do that. Minitab will do it for us.

  1. Choose Data / Unstack Columns
  2. Unstack the data in the weight column
  3. Use the subscripts in the coin column
  4. Store the unstacked data after the last column in use
  5. Name the columns using the unstacked data.
  6. Click OK
  7. Edit the labels on the column so they don't have "weight_" in them. This will make more sense after you get to this step, but the results after unstacking the columns will be like "weight_penny" and I want it changed to just be "penny"

Saving Your Project

Now that you have made the changes to the data, you'll want to save them so that you don't have to make them the next time you work with the data.

  1. Choose File / Save Project As
  2. You should still be in the coins folder on the U: drive, but if not, make sure you are.
  3. [ Optional ] - Create a folder for your group. Name the folder with the name(s) of the people in your group. After creating the folder, change to that folder. From here on, make sure you save all of your work into this folder to keep your files together.
  4. For the file name, use a name that is representative of your group. Do NOT name the file "coins" or "minitab" because there's no way to know whose file that is. If you created a folder in step 3, then you have more lee-way on to name the files.
  5. Click Save

From now on, when you need to work with the Minitab data for this project, open the Project you just saved, not the original worksheet.

3. Creating Boxplots

Side by Side Boxplots

  1. Choose Graph / Boxplot
  2. You have One Y with Groups
  3. The graph variable is weight
  4. The categorical variable is coin
  5. Add an appropriate title by clicking on labels
  6. Click OK

Once you have generated the graph, copy and paste it into Word.

Separate Pane Boxplots

The data for the coins is so diverse that each box plot is a tiny section of the graph and very little detail can be shown about each coin. A better graph would be created as follows.

  1. Choose Graph / Boxplot
  2. You have One Y, Simple
  3. The graph variables are penny, nickel, dime, and quarter
  4. Add an appropriate title by clicking on labels
  5. Choose Multiple Graphs and show the variables as separate panes of the same graph
  6. Click OK

Once you have generated the graph, copy and paste it into Word.

4. Graphical Summaries

Using By Variables

While could create a graphical summary of the weight using the coin type as the by variable, Minitab places all graphs on the same scale when we do this. That means that we'll get results much like we did with the first kind of boxplot graph. Correct, but not very useful.

So, do the following, but then close the graphs without copying them into Word. I just want you to see what it looks like and why you don't want to do this.

  1. Choose Stats / Basic Statistics / Graphical Summary
  2. Use the variable weight
  3. By the variable coin
  4. Click OK

Using Separate Variables

The last graphs were ugly, weren't they? They histograms really didn't show us much at all. Close those graphs and don't save them.

Do this instead.

  1. Choose Stats / Basic Statistics / Graphical Summary
  2. Use the variables penny, nickel, dime, and quarter
  3. Do not put anything in the by variable box
  4. Click OK

Copy and paste each graph into Word.

When you describe the shape, center, and spread, be sure to talk about outliers and if you think that any group mis-measured or mis-recorded the data. Address the other issues mentioned in question 4.

5. Normally Distributed?

The graphical summary can be used to answer two parts of this question, so in your text, refer back to the graphical summaries in question 4, you don't need to re-copy the graphs for this question.

Histograms

Look at the histograms in the graphical summary for each coin. Talk about whether or not it has the shape it's supposed to have.

Normal Probability Plot

This is the one part that isn't generated in the graphical summary, so you'll need to generate those.

  1. Choose Graph / Probability Plot
  2. Pick a single probability plot
  3. The graph variables are penny, nickel, dime, and quarter
  4. Under Multiple Graphs, show the graph variables in separate panes of the same graph
  5. Under labels, give it an appropriate title (you can always edit the title later by double clicking on the title in the graph).
  6. Click OK
  7. The legend on the right side doesn't display all of the data. There are two options.
    1. Since the information is already displayed on the graphical summary, you could just delete the legend.
    2. You can single click the legend box, then grab the box at the top in the center and drag it taller so all of the legend is displayed.

Address what you're looking for in a normal probability plot to tell whether or not the data is normally distributed.

Anderson-Darling Normality Test

The Anderson-Darling Normality tests assumes the data has a normal model and then gives you a p-value, which is the chance of getting your data if it really has a normal model. Anything less than 5% is considered unusual, which means the assumption (that it has a normal model) is wrong. If the p-value is greater than 5% (0.05), then it could just be random fluctuations and there is not enough evidence to reject the normal model assumption (so we'll continue on assuming it is normal in the lack of evidence otherwise).

The p-value is given on both the graphical summary and the legend from the probability plots, so you don't need to do any additional graphs for this, just refer to the ones you already have.

Suggested Order for this Question

Since the grapical summary is already shown in question 4 and the normal probability plots show up on the same graph, I would start the question, show the probability plots, and then address the coins one by one. For each coin, talk about the histogram, probability plot, and Anderson-Darling test. Then move on to the next coin type.

6. Confidence Intervals

The graphical summary includes a confidence interval for the mean. It is shown below the graph as a blue line and it is also shown in the legend on the right as two numbers. For example, it might say "95% Confidence Interval for Mean" and then have the two numbers "4.3256 4.6324" beneath that. The proper way of writing the confidence interval is to say that the population mean (represented by the Greek letter mu) is between those two numbers. That is, 4.3256 g < μ < 4.6324 g (the g is for grams). That gives you the interval of weights the operator should accept. However, since we're not really into confidence intervals until the second half of the class, at this point, you could write it so people understand it and say something like "The operator should accept and nickel between 4.3256 g and 4.6324 g" (assuming the confidence interval was for nickels).

Address whether the claimed value from the Mint falls inside the interval. If it doesn't talk about what might have gone wrong so it doesn't.

7. Test the US Mint's Claim about the Mass of each Coin

Minitab released a service pack that changed the way this screen works. I have patched my home computer to version 14.20, but the classroom computers are still running 14.13. At some point, I will ask the computer technicians to upgrade the software so these instructions may change depending on when you work on it. I'm going to try and give instructions for both versions. You can tell which version you have by clicking Help / About Minitab and looking at the Installed Products on the left. You can also tell because one set of instructions below won't look like what you have on the screen and the other will.

Version 14.13 of Minitab

Repeat this process for each type of coin.

  1. Choose Stat / Basic Statistics / 1 Sample T
  2. Tell it the sample is in the penny column (change penny to nickel, dime, or quarter depending on which coin you're using).
  3. Click Options. Under Test Mean, enter the value the US Mint claims the weight of that type of coin is.
  4. Click OK

Version 14.20 of Minitab

Repeat this process for each type of coin.

  1. Choose Stat / Basic Statistics / 1 Sample T
  2. Tell it the sample is in the penny column (change penny to nickel, dime, or quarter depending on which coin you're using).
  3. Check the box to perform a hypothesis test
  4. The hypothesized mean is the claimed value from the US Mint.
  5. Click OK

Either Version

Copy the output of the hypothesis test into Word.

Look at the p-value. The p-value is the chance of getting the data we got if the Mint's claim is right. Anything below 5% (0.05) is considered too unusual to happen by chance alone, so we have enough evidence to reject the Mint's claim. If the p-value is above 5%, then we'll consider our data is within the realm of normal random fluctuations and we don't have enough evidence to reject the Mint's claim, which means we'll retain (keep on believing it for now) the claim.

8. Differences in Mints

Preparing the Data

We need to once again unstack the data, but this time including the mint as one of the categories.

  1. Choose Data / Unstack Columns
  2. Unstack the data in the weight column
  3. Using the subscripts in the coin and mint columns (select both variables in that order)
  4. Store the unstacked data in a new worksheet
  5. Name the columns containing the unstacked data
  6. Click OK

This will create a new worksheet with variables that have labels like "weight_penny-Denver" and "weight_penny-Philadelphia".

Edit the labels to shorten them up. As they are, they're too long to tell apart in the output. Change them to things like "penny_D" or "penny_P" (repeat for nickel, dime, and quarter).

Conducting the Test

Repeat this process for each type of coin.

  1. Choose Stat / Basic Statistics / 2 Sample T
  2. Your data are in different columns
  3. The first column is penny_D (use nickel, dime, or quarter when appropriate)
  4. The second column is penny_P (use nickel, dime, or quarter when appropriate)
  5. Click OK

Copy the output to Word. The assumption here is that there is no difference in the weights of the two mints, that is the weights are equal. Use the p-value as described in question 7 to make your decision. If the p-value is small (less than 5%) then reject the assumption that they're equal, which means there is enough evidence to show a difference in the mints for that coin. If the p-value is not small (more than 5%) then retain the assumption that they're equal, which means there's not enough evidence to show a difference in the mints for that coin type.