# Minitab Instructions for Chapter 10 Technology Exercise

## M&M Colors (Question 1)

### Finding the claimed proportions

1. Go to the M&M website at http://www.mms.com/
3. Choose Products
4. Choose Peanut M&Ms
5. The claimed percentages are given, but the web page is not accessible, so if you're color blind, have your partner look at the page and send a note to M&M Mars letting them know that their page isn't accessible.

### Finding the critical value (part d)

1. Choose Calc / Probability Distributions / Chi-Square
1. Select Inverse cumulative probability
2. The degrees of freedom is one less than the number of categories
3. The input constant is 0.95, the area to the left of the critical value (this is a right tail test with α = 0.05, but Minitab needs the area to the left).
4. Click OK
2. The critical value is what Minitab calls X

### Finding the test statistic and p-value (parts e & f)

1. Label the first column as Color and enter the names of the colors
2. Label the next two columns in as Observed and Claimed
3. In the Observed column, enter the observed frequencies from Classroom Activity 7. Be sure you use the data for your section.
4. In the Claimed column, enter the percents as claimed from M&Ms. You may enter them as percents or proportions, but do not actually put the % sign in there.
5. Choose Stats / Tables / Chi-Square Goodness-of-Fit Test (One Variable)
1. The observed counts are in the Observed column.
2. The category names are in the Color columns
3. You are testing proportions specified by historical counts. These counts are in the claimed column. (If you put in proportions instead of percents, you can still use this or you can use "specific proportions" and the output will be a little less cluttered).
4. Click on Graphs and turn all graphs off.
5. Click OK

The results have a Chi-Sq, which is your test statistic and a P-value, which is your p-value. The "expected" column contains the expected frequencies.

## Amtrak Delays (Question 2)

### Gathering the Data

Amtrak keeps data available for the last five (5) days only. Since you need at least six days of information, you will need to collect information on more than one date. Do NOT wait until this is due to start it.

1. Visit the Amtrak website at http://www.amtrak.com/
2. The center portion of the screen is split into two parts, Fare Finder and Train Status. Go to the Train Status section.
1. Leave the Departs box empty
2. Put CHI in the Arrives box
3. Put 300 in the optional Train No box.
4. Click Next
3. Record the delay in minutes for the indicated date. If the train is early, record the delay as negative. If the delay is given in hours and minutes, you need to convert it into minutes before recording.
4. Change the date to a previous day and click Resubmit
5. When you are done with the 300 train, change the train number to 22 and go through the cycle with the different dates.
6. When you are done with the 22 train, change the train number to 324 and repeat the cycle of dates.

### Entering the Information into Minitab

When entering information into Minitab, ignore any missing data. Do not put blank rows in the Minitab data.

1. Label two columns in Minitab as train and delay.
2. Enter either the train number or the train name in the first column as many times as you have data for that train. That is, if you have 7 days worth of information for the 300 train, then enter 300 or "Lincoln Service " 7 times into the train column. Repeat this for the other two trains.
3. Enter the delay information for each of the trains into the delay column. Match up the information so that the delay is in the same row as the proper train number.

### Summarize the Delay Times (part c)

1. Choose Stat / Basic Statistics / Display Descriptive Statistics
1. Describe the variable delay
2. By the variable train
3. Click on Statistics and enable any other statistics you might need
4. Click OK
2. Record the values for the 300, 22, and 324 trains in the appropriate columns. Note that Minitab is going to put the trains in numerical order, not the order they appear in the table.
3. Choose Stat / Basic Statistics / Display Descriptive Statistics
1. Describe the variable delay
2. Remove train from the by variables box
3. Click OK
4. Record the values in the combined column of the table.

### ANOVA table (parts d, f, and g)

1. Choose Stat / ANOVA / One-Way (the first option, not the unstacked option)
1. The response variable is delay
2. The factor is the train
3. Click OK
2. Copy the results into the ANOVA table. Notice that the order of the columns is different than what is on your worksheet.

The MS(Total) value does not appear in the ANOVA table output in Minitab as it is not technically part of the ANOVA. However, find it by dividing the SS(Total) by df(Total).

The test statistic and p-value are the F and p-value values from the table.

### The Critical F value (part e)

The F value was found by dividing the MS(Factor) by MS(Error) where the Factor in this problem is the Train. The numerator df is the df(Factor) and the denominator df is the df(Error). You'll need those values to look up the Critical F value.

1. Choose Calc / Probability Distributions / F
1. Choose Inverse cumulative probability
2. The numerator degrees of freedom are the df(Factor)
3. The denominator degrees of freedom are the df(Error)
4. The input constant is 0.95 (the area to the left for an α = 0.05 significance level)
5. Click OK
2. The critical value is the value Minitab calls X