AP statistics practice question

Question 2 Allotted time: 15 minutes (plus 5 minutes to submit) Students at an agricultural station conducted a study to compare genetically modified (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. The table shows summary statistics for the yields, in bushels per acre, and the difference in yield (GM minus regular) for each plot. Standard Mean Deviation Minimum Q1 Median Q3 Maximum GM 125.018 13.623 33 107.4 111.9 127.5 138.0 144.0 Regular 120.482 10.321 33 102.9 111.0 119.4 129.0 133.5 Difference 4.536 6.444 33 -2.1 -0.9 3.0 6.0 20.1 (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 differences in yield is shown below. O -5 10 15 20 25 Difference in yield (bushels per acre, GM minus regular) (c) Describe the distribution of the differences. AP Statistics 2020 Exam | Sample Question The students conducted a test of the hypotheses H : H =0 H : H, # 0, where u, is the population mean difference (GM minus regular) in yield, in bushels per acre, for plots similar to those used in the study. The conditions for inference have been met. (d) One of the conditions for inference that was met is that the sample size of the differences is greater than 30. Explain why it is necessary to satisfy this condition. (e) The test resulted in a p-value of 0.0003. Based on the p-value, what conclusion should the students make