Minitab Instructions for Chapter 10 Technology Exercise

Seatbelt Safety (Question 2)

Start a new worksheet for this problem.

  1. Label columns as year, seatbelt, and fatality
  2. Gather the information for 1985 through 2003 from Figure 1 of the June 2005 Safety Belt Usage in Illinois. This information is from the Illinois Department of Transportation and is at http://www.dot.state.il.us/trafficsafety/seatbelt%20june%202005.pdf. The data is in a chart, so you'll have to read the percents from the top of the bars. Data is available as late as 2005, but we're only able to get information through 2003 for the next part, so we'll stop in 2003.
  3. Gather the information for 1985 through 2002 from the Illinois 2002 Toll of Motor Vehicles Crashes page from the National Highway Traffic Safety Administration at http://www.nhtsa.dot.gov/STSI/State_Info.cfm?Year=2002&State=IL. There is a table toward the bottom of the page that is titled "Fatalities and Fatality Rate per 100 Million VMT". You want the Total Fatality Rate column. Be sure you use the "Fatality Rate" column and not the "Fatalities" column. After gathering the data for 1985 through 2002, click on the 2003 at the top right of the page where it says Change Year. You are looking for the "Fatality Rate per 100M VMT" for Illinois in 2003. It's the second row in the first table. The data for 2004 is not available, so we're going to stop with 2003.

Making the Fitted Line Plot (part b)

  1. Choose Stat / Regression / Fitted Line Plot
  2. The response variable is fatality
  3. The predictor variable is seatbelt
  4. Click OK
  5. Copy the graph and paste it into Word

The Fitted Line plot also contains the regression equation and the value of r2, the percent of the variation that can be explained by the regression model. The output in the session window on Minitab gives much of the same information including an ANOVA table that contains the F test statistic and the p-value that can be used for checking correlation.

Checking for Significant Linear Correlation (parts d & e)

While the p-value can be found from the ANOVA table, it doesn't give the value of r, the correlation coefficient.

  1. Choose Stat / Basic Statistics / Correlation
  2. The two variables are seatbelt and fatality (order doesn't matter)
  3. Click OK

The output gives you the correlation coefficient first and the p-value second. The null hypothesis is that there is no significant linear correlation.

Give the Regression Equation (part h)

If you determined that there was significant linear correlation (positive or negative) by rejecting the null hypothesis of no significant linear correlation, then you should use the regression equation given by the computer. This was found when you did the fitted line plot. Your equation should look something like "fatality = 3.03814 - 0.0230872 seatbelt" (probably not that exactly).

  1. Choose Stat / Regression / Regression
    1. The response variable is fatality
    2. The predictor variable is seatbelt
    3. Click OK
  2. The regression equation is given towards the top of the output, you may need to scroll up.

If, however, you decided that there was no signficant linear correlation because you retained the null hypothesis of the correlation test, then you should use the mean of y (y-bar) for the estimated equation. Your equation should be something like "fatality = ####" where #### is the numerical value of the mean of the fatality variable. You'll have to do descriptive statistics to find out what that is.

Amtrak Delays (Question 3)

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 "State House" 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

Go to the Math 113 technology project page.

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Last updated December 6, 2005 10:00 AM