Project C.I. for Small Samples

The Illinois State Racing Commission monitors horse racing at all the state racetracks and Summer county fairs.  In each race, the winning horses and a randomly selected horse are checked for performance enhancing drugs.  Blood and urine samples are collected by a veterinarian and sent to the state lab.  One test that is performed is a blood-gas analysis.  This test measures the amount of Carbon Dioxide (CO2) in the blood.  If the CO2 level is 37 millimoles or more per liter for a nonlasix horse or 39 millimoles per liter or higher for a lasix horse, the horse is in violation.  This can lead to the owner forfeiting his winnings, paying a fine and serving a suspension.

Given the tested horses in 3 races had blood samples with CO2 levels of 
Race 1
Horse 1 (Lasix): 39.2, 39.4, 39.0 and 39.1 millimoles per liter
Horse 2 (Nonlasix):  36.2, 36.5, 37.0, 36.0 millimoles per liter
Horse 3 (Lasix):  37.9, 38.0, 37.4, 38.1 millimoles per liter
Horse 4 (Nonlasix):  37.1, 37.2, 37.3, 37.4 millimoles per liter

ti-83.gif (1031 bytes)

Use your TI-83 calculator determine the t-interval for the mean CO2 level for each horse.
  1.  Choose "STAT".
  2.  With "EDIT" highlighted select "1:Edit" by pressing "ENTER".
  3.  If there is data in List 1 (L1) clear it by using the up arrow to highlight "L1". 
       Then press "CLEAR" and "ENTER".  Repeat Step 3 to clear data from List 2
       (L2), List 3(L3), and List 4 (L4).
  4.  Enter the 4 CO2 readings for horse #1 into L1 by entering each value and
        pressing "ENTER" after each value.  Similarly enter the 4 CO2 readings for
        horse #2 into L2, the 4 CO2 readings for horse #3 into L3, and  the 4 CO2
        readings for horse #4 into List L4.
  5.  Press the buttons "2nd" and "MODE" (QUIT) to signify the end of the data.  

  6.  Choose "STAT".  Use the right arrow to highlight "TESTS".
  7.  Use the down arrow to choose "8:TInterval" and press "ENTER". 

   8.  Use the arrow key to highlight "Data" and press "ENTER".
   9.  Use the down arrow and press "2nd" "1" to submit  (L1) as List 1 and press
        "ENTER".
 10.  Enter "1" for the Frequency and press "ENTER".
 11. Enter "0.95" for the C-Level (confidence level) and press "ENTER".
 12.  With "Calculate" highlighted, press "ENTER". 

   13.  The 95% confidence interval for the population mean is 
           38.903 <  < 39.447

   14.  Repeat steps 6 through 13 for horses 2, 3 and 4.  
          Note:  In step 9, enter  "2nd" "2" to submit  L2, "2nd" "3" to submit  L3,
                      and "2nd" "4" to submit L4.

Nonlasix horses have a limit of 37 and Lasix horses have a limit of 39.  The entire interval must be over the limit for a horse to be in violation.  This is the policy of the Illinois Racing Board.

Horse 95% Confidence Interval Violation
1 Lasix 38.903 < mu < 39.447 NO
2 Nonlasix 35.733 < mu < 37.117 NO
3 Lasix 37.355 < mu < 38.345 NO
4 Nonlasix 37.045 < mu < 37.455 YES

Race 2
Horse 1 (Lasix): 39.2, 39.8, 39.6 and 39.1 millimoles per liter
Horse 2 (Nonlasix):  36.4, 37.8, 37.2, 36.3 millimoles per liter
Horse 3 (Lasix):  41.0, 39.2, 40.1, 39.1 millimoles per liter
Horse 4 (Nonlasix):  37.7, 37.5, 37.1, 37.2 millimoles per liter

Using "TInterval" on the calculator
Nonlasix horses have a limit of 37 and Lasix horses have a limit of 39.

Horse 95% Confidence Interval Violation
1 Lasix 38.899 < mu < 39.951 NO
2 Nonlasix 35.797 < mu < 38.053 NO
3 Lasix 38.436 < mu < 41.264 NO
4 Nonlasix 36.937 < mu < 37.813 NO

Race 3
Horse 1 (Lasix): 39.8, 40.4, 38.0 and 39.7 millimoles per liter
Horse 2 (Nonlasix):  37.2, 37.5, 37.0, 36.4 millimoles per liter
Horse 3 (Lasix):  40.0, 39.6, 39.2, 40.1 millimoles per liter
Horse 4 (Nonlasix):  37.1, 37.2, 37.1, 37.0 millimoles per liter

Using "TInterval" on the calculator
Nonlasix horses have a limit of 37 and Lasix horses have a limit of 39.

Horse 95% Confidence Interval Violation
1 Lasix 37.835 < mu < 41.115 NO
2 Nonlasix 36.286 < mu < 37.764 NO
3 Lasix 39.071 < mu < 40.379 YES
4 Nonlasix 36.97 < mu < 37.23 NO

Note:  This is one of tests used used by the Illinois Racing Commission for harness and thoroughbred race horses.

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