Question

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
hours with a 9.4
​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

Interpretation: the sample mean battery life is 9.4 hours (n = 24, s = 0.25). Consumers claim the true mean is less than 10 hours, so use a one‑sample t test.

Hypotheses
- H0: μ = 10
- Ha: μ < 10

Test statistic
t = (x̄ − μ0) / (s/√n) = (9.4 − 10) / (0.25/√24)
= −0.6 / 0.05103 ≈ −11.76, with df = 23.

p‑value
For df = 23, P(T ≤ −11.76) is essentially 0 (p < 0.0001).

Conclusion
Reject H0. There is extremely strong evidence that the true mean battery life is less than 10 hours, so the manufacturer’s claim is false.

(Assumptions: sample is random and t‑test requires approximate normality of battery life; with n = 24 the test is reasonably robust.)