Probability in Catching Fish

     In this discussion, you will use an Excel data set containing the "width percentage" of a group of perch, a type of fish.  The width percentage is found by multiplying the width by one hundred, then dividing the result by the length.  The mean of the data set is 16.18 and the standard deviation is 1.13. Using the java applet provided by Duxberry Press (©1999), you can analyze the probabilities for a normal distribution of this data set.

1. Click on this link to start the applet.
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2. Fill in the mean, standard deviation, start and
end points shown in figure 1.
    *Note that the probability (Prob) = 0.95 for this data range. The probability is shown by the shaded area under the curve. The probability means that if you were catching fish from this population, 95 out of 100 fish would have width percentages within the range of 13.965 - 18.395.
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3. Enter a Start value of 0 and an End value of 13.965.  Now the area shaded under the curve has a probability of .025.
 
Now enter a Start value of 18.395 and an End value of 32.36 (any large number will work). The area under the curve again has a probability of .025.

So, combining these two cases, if you were catching fish from this population of perch, only 5 out of 100 fish would have "width percentages" below 13.965 (very thin fish) or above 18.395 (very fat fish).
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4. So, let's say you are fishing and catch a fish with a "width percentage" of 13.3.  Since its width percentage falls in that area under the curve where a fish from the population would only be caught 2.5 times out of 100, it is unlikely that the fish is a perch. It is too thin! Is it a perch from this population? So, if you say, "This fish is a perch," you would be correct 2.5 times out of 100. However, you would be wrong 97.5 times out of 100! What if you made the opposite choice and said, "This fish is too thin; it is not a perch?" Now you would be correct 97.5 times out of 100 and incorrect only 2.5 times out of 100. Which would you rather be, right 97.5 times out of 100 or wrong 97.5 times out of 100?
 

Probability is a key concept in statistical hypothesis testing. It relates to the risk researchers are willing to take when they choose one hypothesis over another. How does this discussion relate to hypothesis testing?

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