Question

answer in the simplest form and like a teen
A manufacturer claims that their battery for a particular cell phone model ​lasts 10
hours.
​
​However, consumers complained that the batteries lasted ​less than 10
hours.
​
​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.
​
​Based on the data given, is there evidence ​that the manufacturer’s claim is false?
​Justify your answer.

Answer 1

Short answer: Yeah — the data say the claim is false.

Why (simple steps):
- Hypotheses: H0: μ = 10 hours (manufacturer right). Ha: μ < 10 hours (consumers right).
- Use a t-test (n = 24, σ unknown).
- Test statistic: t = (9.4 − 10) / (0.25 / √24) ≈ −11.76.
- With df = 23 that t gives a p-value basically 0 (way less than 0.05).

Conclusion: Reject H0. The sample gives strong evidence the true mean battery life is less than 10 hours.

(Also, a 95% CI for the mean is about 9.294 to 9.506 hours, which is well below 10.)