SME
Grade 12 Math · Problem type
Which alternative hypothesis?
Use this for “Write H₀ and Hₐ for the claim that the new bulbs last longer.”
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Which Hₐ does the claim call for?
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Assumptions
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H₀ always says “equal”: the mean is still μ₀. Hₐ is what the study hopes to show.
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Words like “more”, “longer” or “increased” give Hₐ: μ > μ₀; “less”, “fewer” or “shorter” give μ < μ₀.
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“Changed”, “different” or “no longer” with no direction give Hₐ: μ ≠ μ₀, a two-sided test.
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Related lessons
Hypothesis tests for one and two samples
Main lesson
One-mean z-test
Use this for “Is the mean less than μ₀?” (or more than, or different from) with σ known.
One-mean t-test
Use this for “A sample of 16 has mean 496 g and s = 8 g. Is the mean different from 500 g?”
Matched pairs t-test
Use this for “Twelve students gained 2.5 points on average after a review, s = 3.2. Did the review change scores?”
Two-proportion z-test
Use this for “84 of 150 people sent a reminder voted, against 66 of 150 who were not. Is there a difference?”
Two-sample t-test for means
Use this for “Do two groups have different means?” from two independent samples.
Type I or Type II error?
Use this for “Name a Type I and a Type II error for this test.”