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2020 Exam
Sample Question
AP ® STATISTICS Note: This is an example of 2020 Question 2, a multi-focus free-response item with allotted time of 15 minutes (plus 5 minutes to submit). Question 1 is a longer multi-focus free-response item, with allotted time of 25 minutes (plus 5 minutes to submit).
Question 2
Allotted time: 15 minutes (plus 5 minutes to submit) Students at an agricultural station conducted a study to compare genetically modi ed (GM) corn with regular corn. Each of 33 plots of land was divided into two half-plots; one half-plot was randomly selected to be planted with the GM corn, and the other half-plot was planted with the regular corn. e table shows summary statistics for the yields, in bushels per acre, and the di erence in yield (GM minus regular) for each plot. Mean
Standard
DeviationMinimumQ1MedianQ3Maximum
GM125.01813.62333107.4111.9127.5138.0144.0
Regular120.48210.32133102.9111.0119.4129.0133.5
Ƭ4.5366.44433-2.1-0.93.06.020.1
(a) Explain why the yields from one type of corn are not independent of the yields from the other type of corn. (b) Based on the summary statistics, would it be more likely to obtain a yield of 123 or more bushels per acre from a plot of GM corn or a plot of regular corn? Justify your answer. A boxplot of the di erences in yield is shown below. Di erence in yield (bushels per acre, GM minus regular) (c) Describe the distribution of the di erences.
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?e students conducted a test of the hypotheses H 0 :µ d =0 H a :µ d 0, where µ d is the population mean di erence (GM minus regular) in yield, in bushels per acre, for plots similar to those used in the study. e conditions for inference have been met. (d) One of the conditions for inference that was met is that the sample size of the di erences is greater than 30. Explain why it is necessary to satisfy this condition. (e) e test resulted in a -value of 0.0003. Based on the -value, what conclusion should the students make?
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