Testing Claims about Means — Test

Question 1 • Statistics

What are the hypotheses the teacher should use?

Answer

ratio of cap h sub 0 to line segment x sub dom is equal to line segment x sub nondom , ratio of cap h sub A to line segment x sub dom is equal to line segment x sub nondom

ratio of cap h sub 0 to mu sub dom is equal to mu sub nondom , ratio of cap h sub A to mu sub dom is not equal to mu sub nondom

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

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

Explanation

For a paired comparison, define μ_diff as the population mean of the differences between the two measurements. The null hypothesis says there is no average difference, so H₀: μ_diff = 0; a two-sided alternative says the average difference is not zero, so Hₐ: μ_diff ≠ 0. These are the hypotheses in choice D.

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