Project C.I. for Small Samples

The racehorse has been highly optimized over hundreds of years of breeding to be an extremely efficient runner. However many of the species suffer from bleeding in the lungs under the stress of running.  "Lasix", is a powerful diuretic that causes fluids locked up in the horse's body tissues to be released and expelled in the urine. This has the effect of lowering the horse's blood pressure, particularly in the aorta and pulmonary artery. The lower blood pressure in the capillaries mitigates the problem of bleeding, thus, the horse's performance returns to a normal level.  In addition, Lasix has the side effect of increasing the Carbon Dioxide (CO2) in the blood.

 

The Illinois State Racing Commission monitors horse racing at all the state racetracks and Summer county fairs.  In each race, the 3 horses "finishing in the money" (Win, Place, Show) 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 and tested for various illegal performance enhancing drugs. 

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.  4 samples of blood are taken from each of the 4 horses.

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

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

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

A.  Find a 95% confidence levels for the CO2 level in each horse.

B.  Is any horse in violation (the entire interval is above the legal limit)?
     Note:  This is one of tests used used by the Illinois Racing Commission for
                harness and thoroughbred race horses.

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