Question

A manufacturer claims that their battery for a particular cell phone model lasts
10
10 hours.

However, consumers complained that the batteries lasted less than
10
10 hours.

The manufacturer randomly sampled
24
24 batteries and found that the mean battery life of the sample was 9.4
9.4
9.4 hours with a
standard deviation of
0.25
0.25 hours.

Based on the data given, is there evidence that the manufacturer’s claim is false?
Justify your answer. answer the question make it short

Answer 1

Let H0: μ = 10 vs Ha: μ < 10. Test statistic
t = (9.4 − 10) / (0.25/√24) = −0.6 / 0.05102 ≈ −11.76 (df = 23).
The one‑sided p‑value ≪ 0.001.

Conclusion: reject H0. There is very strong evidence the mean battery life is less than 10 hours.