Feat of Strength #6

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The Drole Pineapple Company managers are always interested in the sizes of the pineapples grown in the company’s fields, because bigger and juicier pineapples means bigger and juicier wallets. As any company would, the Drole Pineapple Company is very conscious about maximizing its profits as much as possible, and for or Drole, advertising the succulent size of its pineapples is a key factor to its sales strategy. Thus, managers of the company are interested in finding the largest pineapples in its harvested batch to put into the market to uphold its reputation of having the largest pineapples in the business. The managers of Drole are currently trying to argue that the mean weight of the pineapples harvested last year is actually greater than the previously recorded 31 ounces; a greater mean weight would mean greater profits and advertising power for the company. So through various calculations, I will determine whether the company is correct in its claim and grant whether or not Drole deserves its title for harvesting the largest pineapples in the country.

The Drole Pineapple Company claims that the mean weight of its pineapples harvest last year is greater than 35 ounces, and not in fact the 31 ounces it was recorded to be. To test its claim, we will select a single pineapple at random from last year’s crop and determine the approximate probability that it weighs more than 35 ounces. The population of interest is the pineapples harvested from last year’s crop, and we want to test a claim about the mean weight µ for these pineapples. The null hypothesis is that the mean weight of pineapples Drole harvested last year is 31 ounces (µ = 31), and the alternative hypothesis is that the mean weight is greater than 35 ounces (µ > 35). In other words, we are trying to see whether there is enough evidence to prove that the mean weight is in fact 35 ounces and reject the old claim that it was 31 ounces. However, before constructing any confidence interval about an...
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