Chuck wants to know which brand of tire, cap A or cap b , lasts longer on cars. He chooses 32 cars and puts brand cap A on one side of the car and brand cap b on the other side. The side that receives brand cap A is determined by a coin toss. After three months, Chuck measures the amount of tread on all tires to determine if, on average, there is a difference open paren brand A minus brand B close paren in tread wear. What are the hypotheses Chuck should use?
Answer
A
ratio of cap h sub 0 to line segment x sub cap A is equal to line segment x sub cap b ; ratio of cap h sub A to line segment x sub cap A is not equal to line segment x sub cap b
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 not equal to 0
C
ratio of cap h sub 0 to mu sub cap A is equal to mu sub cap b ; ratio of cap h sub A to mu sub cap A is not equal to mu sub cap b
D
ratio of cap h sub 0 to line segment x sub diff is equal to 0 ; ratio of cap h sub A to line segment x sub diff is not equal to 0
Explanation
Because each car gets both tire brands, the data are paired. Define the difference for each car as brand A minus brand B, and let μ_diff be the population mean of those differences. Since Chuck wants to test whether there is any average difference, the hypotheses are H₀: μ_diff = 0 and Hₐ: μ_diff ≠ 0, which is choice B.
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