The alternative hypothesis is

Question

BlackTom AI · Accepted Answer

Higher illumination is predicted to decrease mean task completion time, so the alternative is H1: μ_high < μ_low.

1. Relevant knowledge points and concepts
- Define population means: μ_high = mean task time under higher illumination; μ_low = mean task time under lower illumination.
- Hypotheses: the null hypothesis H0 is the statement tested (usually the complement of H1). For a one-tailed (directional) alternative, H0 is the non-directional complement.
- One-tailed vs two-tailed: a directional claim (less than or greater than) leads to a one-tailed alternative; “different” leads to a two-tailed alternative.

2. Step-by-step reasoning
- The wording in option (a) explicitly states a directional prediction: higher illumination yields lower mean time than lower illumination.
- Translate into symbols: H1: μ_high < μ_low.
- The null must be the complement: H0: μ_high ≥ μ_low (which often is tested as H0: μ_high = μ_low with the alternative as <, but logically the null is the "no decrease" case).

3. Intermediate steps (formal statements)
- Set variables: μ_H ≡ μ_high, μ_L ≡ μ_low.
- Alternative: H1: μ_H < μ_L.
- Null (complement): H0: μ_H ≥ μ_L (or for practical testing H0: μ_H = μ_L with alternative μ_H < μ_L).

4. Why the correct answer is correct
- Option (a) matches the directional prediction (higher illumination reduces time) and corresponds exactly to H1: μ_H < μ_L. This is the precise alternative hypothesis expressed in words.

5. Why other options are incorrect
- (b) states the opposite direction (higher illumination increases mean time): H1: μ_H > μ_L, which contradicts the prediction.
- (c) “equal mean” is not an alternative hypothesis; it is the null hypothesis (no effect).
- (d) “different mean” is non-directional (two-tailed: μ_H ≠ μ_L) and does not capture the specific predicted decrease.

6. Conclusion
Option (a) is the correct alternative hypothesis: The higher level of illumination has lower mean task completion time than the lower level of illumination. This matches the provided answer.

The alternative hypothesis is单项选择题

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