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In a simple random sample of 250 father-son pairs taken from a large population of such pairs, the mean height of the fathers is 68.5 inches and the SD is 2.5 inches; the mean height of the sons is 69 inches and the SD is 3 inches; the correlation between the heights of the fathers and sons is 0.5. In the population, are the sons taller than their fathers, on average? Or is this just chance variation? The SE of the mean difference between heights of fathers and sons in the sample is closest to 0.176.
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