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