Question

Students at an agricultural station conducted a study to compare geneticallymodified (GM) corn with regular corn. Each of 33 plots of land was divided intotwo half-plots; one half-plot was randomly selected to be planted with the GMcorn, and the other half-plot was planted with the regular corn.The table shows summary statistics for the yields, in bushels per acre, and thedifference in yield (GM minus regular) for each plot.MeanStandardDeviation n Minimum Q1 Median Q3 MaximumGM 125.018 13.623 33 107.4 111.9 127.5 138.0 144.0Regular 120.482 10.321 33 102.9 111.0 119.4 129.0 133.5Difference 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.

Answer 1

Explanation:

The given data is represented in the attachment.

a) Explain why yields from one type of corn are not independent of the yields from the other type of corn.

Yields from one type of corn are not independent of the yields from the other type of corn because, as the corns are planted in two similar plots, they could compete during watering process, even the amount of nutrients shared and the type of air. This means one corn may get more nutrients than the other. Therefore, they are not independent (they are dependent).

b) Based on the summary statistics, GM is expected to more likely obtain yield greater than 123, because 123 is greater than mean for regular corn but less than mean for GM corn.

Thus,

P(yield>123|GM)>0.5; and P(yield>123|Regular)<0.5