Question 1

Youhavebeen asked to design an experiment for the new fertilizer SuperGrow.Thecompanywantstocomparethefertilizertotheircurrent product OkGrowandtheircompetitor'sproductFastFarm.Theyhave200farmsthat have agreed to participate in the study.There are 101 farms in town K and 99 farms in town L. The town K farms consist of 75 that grow wheat and 26 that grow corn. The town L farms consist of 70 that grow corn and 29 that grow wheat. Youalso want to find the optimal water design for thefertilizers and the farmers haveagreed to take your advice on how often to water:once a day or twice a day.Provide a design for how you suggest allocating the different fertilizers and watering strategies to the 200farms.

Question 2

(a) Provide the definition of a p-value.

(b) Provide an explanation for the standard error of a sample statistic. Some examples in this class would be the standard error of a sample mean or a sample proportion.

(c) State the central limit theorem in words, not formulas.

Question 3

A widget company tested 101,000 widgets, of which only 1,000 had defects. The company's test correctly identified defects 99% of the time and correctly identified non-defects 95% of the time.

1. Whatpercentageofthewidgets markedasdefects doyouexpecttobedefective?
2. What percentage of the widgets marked as non-defects do you expectto be notdefective?
3. Discuss the answers to (a) and (b). Do you think these percentages are acceptable? If so, explain why. If not, explain why and provide a suggestion on how they could be improved.