A farmer would like to estimate the mean amount of corn produced on the east side of his farm versus the west side of his farm where the soil is different. To do so, he selects a random sample of 20 of the 400 plots of land on the east side of the farm and randomly selects 10 plots of land from the 150 plots on the west side of his farm and measures the amount of corn produced for each plot. Are the conditions for inference met?

Both samples were selected randomly, so the random condition is met. The samples are each less than 10% of their side’s plots: 20 of 400 is 5%, and 10 of 150 is about 6.7%, so the 10% condition is met. But the sample sizes are only 20 and 10, and no information says the corn yields are normally distributed. Therefore, the Normal/large sample condition is not established; choice D is correct.

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