Imagine that a researcher wants to compare the intelligence levels of Poodles to all dogs.  He hypothesizes that Poodles will score differently than other dogs.  He uses a standard test of dog intelligence in his study. The population of all dogs has a mean of μ = 100, and an SD of 15.  He obtains a random sample of 500 Poodles and he finds that the mean intelligence score of the sample is 117.

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