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.

Answer 1

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

Why (simple steps):
- Hypotheses: H0: mean = 10 hours. Ha: mean < 10 hours (consumers’ claim).
- Use a t-test (σ unknown). n = 24, x̄ = 9.4, s = 0.25, df = 23.
- Test statistic: t = (9.4 − 10) / (0.25/√24) ≈ −11.76.
- That t is huge in size, so the one‑sided p‑value is basically 0 (p < 0.0001).

Because the p‑value is far below any normal cutoff like 0.05, we reject H0. In plain terms: the sample gives very strong evidence the true mean battery life is less than 10 hours.