Question

answer in the simplest way so a teen can understand it


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

Keep it simple:

1. What we test:
- H0 (manufacturer right): mean = 10 hours.
- Ha (consumers right): mean < 10 hours (one-sided).

2. Use a t-test (we don’t know true population SD). Compute the t-statistic:
- t = (sample mean − claimed mean) / (s / sqrt(n))
- t = (9.4 − 10) / (0.25 / sqrt(24)) ≈ −0.6 / 0.0510 ≈ −11.76

3. Compare or get p-value:
- With 23 degrees of freedom, a t of −11.76 gives a p-value essentially 0 (much less than common cutoffs like 0.05).

4. Conclusion:
- Because the t-statistic is far into the left tail and the p-value is tiny, we reject H0. There is strong evidence the batteries last less than 10 hours — the manufacturer’s claim is false.