Question 9 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A cell phone manufacturer would like to estimate the mean difference in battery lifespan for a phone in full-power versus power-saver mode. They randomly select eight phones and determine the battery lifespan, in hours, for each phone using each power mode.A 90% confidence interval for the true mean difference (low power battery life – full power battery life) in battery life is 5.42 hours to 6.71 hours. A journalist claims that battery lifespan is, on average, 5 hours longer when the phone is used under low-power mode as opposed to full-power mode. Is this claim supported by the 90% confidence interval?
Answer
A
Yes, 5 is a plausible value in the 90% confidence interval.
B
No, 5 is not a plausible value in the 90% confidence interval.
C
No, 0 is not a plausible value in the 90% confidence interval.
D
Yes, 0 is not a plausible value in the 90% confidence interval.
Explanation
The 90% confidence interval for the mean difference is 5.42 to 6.71 hours. A claimed average difference of 5 hours is not in that interval, so it is not a plausible value according to this confidence interval. Therefore, the claim is not supported; choice B is correct.
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