Question 6 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students who are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. What are the appropriate hypotheses?
Answer
A
H0: μ = 1 versus Ha: μ < 1, where μ = the mean amount of time that the selected students spend doing statistics homework each night
B
H0: μ = 1 versus Ha: μ > 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night
C
H0: μ = 1 versus Ha: μ < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night
D
H0: μ = 1 versus Ha: μ > 1, where μ = the true mean amount of time that the selected students spend doing statistics homework each night
Explanation
The question asks whether the true mean homework time for all statistics students is less than one hour. The null hypothesis uses the claimed value, μ = 1, and the alternative is μ < 1. Because μ refers to the true population mean—not just the six sampled students—choice C is correct.
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