Question 1 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, two hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of five vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. Here are the data (in hours): 2.2, 1.85, 2.15, 1.95, and 1.90. They would like to know if the data provide convincing evidence that the true mean run time differs from two hours. What are the appropriate hypotheses?
Answer
A
H0: μ = 2 versus Ha: μ < 2, where μ = the true mean run time for all vacuums of this model
B
H0: μ = 2 versus Ha: μ > 2, where μ = the true mean run time for all vacuums of this model
C
H0: μ = 2 versus Ha: μ ≠ 2, where μ = the true mean run time for all vacuums of this model
D
H0: μ ≠ 2 versus Ha: μ = 2, where μ = the true mean run time for all vacuums of this model
Explanation
The claim being investigated is whether the true mean run time differs from 2 hours. “Differs” allows for a mean either greater than or less than 2, so the alternative hypothesis is two-sided: μ ≠ 2. The null hypothesis represents the claimed value, μ = 2, making choice C correct.
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