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A company claims that their light bulbs last at least 1000 hours. How would you test this claim?

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To test the company's claim that light bulbs last at least 1000 hours, perform a one-sample hypothesis test:

  1. Hypotheses:
    • Null (H₀): μ ≥ 1000 hours
    • Alternative (H₁): μ < 1000 hours
  2. Significance Level: Set α = 0.05 (5%).
  3. Data Collection: Test a random sample of light bulbs, recording their lifespans.
  4. Calculate Test Statistic: Use a z-test or t-test (depending on whether the population standard deviation is known).
  5. Decision Rule:
    • If the test statistic is less than the critical value (left-tailed test), reject H₀.
    • If the test statistic is greater, do not reject H₀.
  6. Conclusion:
    • Reject H₀: Evidence suggests bulbs last less than 1000 hours.
    • Do not reject H₀: Insufficient evidence to disprove the claim.

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