Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Let mu sub 1 is equal to the true mean travel time to school along route 1 and mu sub 2 is equal to the true mean travel time to school along route 2. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. What are the appropriate hypotheses?
Answer
A
ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is less than 0
B
ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is equal to 0
C
ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is not equal to 0
D
ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is greater than 0 ratio of cap h sub 0 to mu sub 1 minus mu sub 2 is equal to 0 , ratio of cap h sub A to mu sub 1 minus mu sub 2 is less than 0
Explanation
The question asks whether there is evidence of a difference in the two routes’ true mean travel times, without specifying that the difference must be in one direction. So the alternative is μ₁ − μ₂ ≠ 0, while the null is μ₁ − μ₂ = 0. Choice C gives these two-sided hypotheses; Timmy’s belief that route 1 is faster does not change the question’s stated goal of testing for any difference.
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