A study found that 15% of teenagers get the recommended 8 to10 hours of sleep each night. A guidance counselor at a large high school takes a random sample of 80 students and asks them if they get 8 to 10 hours of sleep each night of the school week. Of the 80 students, 15 state they get 8–10 hours of sleep each school night. Which hypotheses would test if the proportion of students at this high school is different from the proportion in the study?
Answer
A
H0:p ≠ 0.19, Ha:p = 0.19
B
H0:p ≠ 0.15, Ha:p = 0.15
C
H0:p = 0.19, Ha:p ≠ 0.19
D
H0:p = 0.15, Ha:p ≠ 0.15
Explanation
The study’s reported proportion is 0.15, so the null hypothesis uses p = 0.15. The question asks whether the high school’s proportion is different, which calls for a two-sided alternative, p ≠ 0.15. Therefore, choice D is correct: H0: p = 0.15 and Ha: p ≠ 0.15.
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