Question

answer in the simplest way


A manufacturer claims that their battery for a particular cell phone model ​lasts 10 hours.
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​However, consumers complained that the batteries lasted ​less than 10 hours.
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​The manufacturer randomly sampled 24 batteries and ​found that the mean battery life of the sample was 9.4 hours with a ​standard deviation of 0.25 hours.
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​Based on the data given, is there evidence ​that the manufacturer’s claim is false?
​Justify your answer.

Answer 1

Let μ = true mean battery life. Test:

- H0: μ = 10 hours
- Ha: μ < 10 hours (consumers’ claim)

Compute t:
- n = 24, x̄ = 9.4, s = 0.25
- SE = s/√n = 0.25/√24 ≈ 0.0510
- t = (9.4 − 10)/SE = −0.6 / 0.0510 ≈ −11.76
- df = 23

This t is far below the one‑tailed critical value (≈ −1.714 at α = 0.05). The p‑value is essentially 0 (p < 0.0001), so reject H0.

Conclusion: There is strong evidence that the batteries last less than 10 hours, so the manufacturer’s claim is not supported.