AnswersStatisticsTesting a Claim about a Mean Difference — QuizQuestion 7
7
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Testing a Claim about a Mean Difference — Quiz

Question 7 • Statistics

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 open paren older minus younger close paren in the times to run the track is negative 15 point 7 seconds with a standard deviation of 8 point 3 seconds. Are the conditions for inference met?

Answer
A
No. The random condition is not met.
B
No. The 10 percent condition is not met.
C
Yes. All conditions are met.
D
No. The Normal/Large Sample condition is not met because the sample size is too small and the shape of the distribution of differences is not known.

Explanation

Because the horses are sampled as sibling pairs, inference should use the 17 paired differences (older minus younger). The random condition is met, but 17 differences is too small to rely on the Large Sample condition, and no information is given about whether their distribution is approximately Normal or has outliers. Therefore, the Normal/Large Sample condition is not established; choice D is correct.

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