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FA25_QTM_100_3 Final Exam- Requires Respondus LockDown Browser

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A hypothesis test about the true proportion was performed using the following hypotheses, which yielded a p-value < 0.05 (suppose all conditions for inference are satisfied): 𝐻 0 : 𝑝 = 0.7 , 𝐻 𝑎 : 𝑝 < 0.7 Which of the following scenarios would yield a similar p-value (i.e., p-value < 0.05) as the initial hypothesis test above?

Options
A.𝐻 0 : 𝑝 = 0.7 , 𝐻 𝑎 : 𝑝 < 0.7 , 𝑧 = 2.08
B.𝐻 0 : 𝑝 = 0.5 , 𝐻 𝑎 : 𝑝 > 0.5 , 𝑧 = − 2.04
C.𝐻 0 : 𝑝 = 0.5 , 𝐻 𝑎 : 𝑝 ≠ 0.5 , 𝑧 = − 2.01
D.𝐻 0 : 𝑝 = 0.6 , 𝐻 𝑎 : 𝑝 > 0.6 , 𝑧 = 2.03
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The question presents a hypothesis test about a true proportion with H0: p = 0.7 and Ha: p < 0.7, and it states that the p-value was less than 0.05. We’re asked to identify which of the given scenarios would yield a similar p-value (i.e., p-value < 0.05). Option 1: H0: p = 0.7, Ha: p < 0.7, z = 2.08 - For a left-tailed test (Ha: p < 0.7), the p-value is the probability of observing a z statistic as extreme or more in the left tail, i.e., p = P(Z ≤ z_obs). - Here z_ob......Login to view full explanation

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