Question

answer in the simplest way and like a teen would understand
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.

also make the math as short and simple as possible

Answer 1

Short answer: Yes — strong evidence the batteries last less than 10 hours.

Work (very short):

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

t = (9.4 − 10) / (0.25 / √24) = −0.6 / 0.0510 ≈ −11.76.

For df = 23, the 5% one-tail cutoff is about −1.714. −11.76 is way smaller, and the p-value is practically 0 (p < 0.0001).

Conclusion: Reject H0. The sample gives very strong evidence the true mean battery life is less than 10 hours (assuming the sample was random).