Exequiel and Sigmund are fishermen constantly trying to outdo each other. At the Willow Pond fishing contest, Exequiel caught fish that weighed 2.5, 3.0, and 3.6 pounds. Sigmund caught fish weighing 4.0 and 4.8 pounds. The average weight of fish caught during the contest (that is, the mean of the population, ) is 3.0 pounds.
At award time, Sigmund claims that he should receive a “rare catch” award. His total catch weight is only 0.3 pound less than Exequiel’s, but his mean weight is higher. Though Sigmund caught 1 less fish, he insists that if Exequiel fished at Willow Pond 100 times, Exequiel would get a catch like Sigmund’s fewer than 10 times.
If you were the judge and had to assess Sigmund’s claim to a rare catch, how would you evaluate this claim? Run a t-test to determine the statistical significance of each sample compared to the population mean of .