An equestrian enthusiast is interested in the racing times of horses. She believes an older horse will have a faster race time than a younger horse. She selects a random sample of 17 sibling pairs of adult horses and records their times for running on the same track. The mean difference (older – younger) in the times to run the track is –15.7 seconds with a standard deviation of 8.3 seconds. Are the conditions for inference met?

This is a paired-data inference because each observation is the time difference within a sibling pair. The pairs were randomly sampled, and 17 pairs would ordinarily be less than 10% of the population of such pairs. However, with only 17 differences, the sample is too small to rely on the Large Sample condition, and the shape of the differences’ distribution is not given. Therefore, the Normal/Large Sample condition is not established; choice C is correct.

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