AnswersStatisticsTesting a Claim about a Mean Difference — QuizQuestion 4
4
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Testing a Claim about a Mean Difference — Quiz

Question 4 • 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. What are the hypotheses the equestrian should use?

Answer
A
ratio of cap h sub 0 to mu sub diff is equal to 0 ; ratio of cap h sub A to mu sub diff is greater than 0
B
ratio of cap h sub 0 to mu sub diff is equal to 0 ; ratio of cap h sub A to mu sub diff is less than 0
C
ratio of cap h sub 0 to mu sub older is equal to mu sub younger ; ratio of cap h sub A to mu sub older is less than mu sub younger
D
ratio of cap h sub 0 to mu sub older is equal to mu sub younger ; ratio of cap h sub A to mu sub older is greater than mu sub younger

Explanation

The difference is defined as older horse time minus younger horse time. If older horses are faster, their times are lower, so this difference should be negative on average. Thus the alternative hypothesis is μ_diff < 0, with the null hypothesis μ_diff = 0; this is choice B.

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