题目
题目

BTRY3010/BTRY5010/STSCI2200/STSCI5200 Lecture #26 Pages ( 126 - 129, 134 )

单项选择题

Researchers are studying whether a high-protein diet reduces mortality in lab mice exposed to a toxin. Among 900 mice on a standard diet, 36 died. Among 950 mice on a high-protein diet, 15 died. Definitions: p1 = proportion of mice that died on the standard diet p2 = proportion of mice that died on the high-protein diet Hypotheses: H0: p1 = p2 (The diet does not affect mortality; both groups have the same mortality rate) H1: p1 > p2 (The diet reduces mortality; mice on the standard diet have a higher mortality rate) What is your decision, and what does it mean in the context of the study?

选项
A.Fail to reject H0; this data is inconsistent with the assumption that there is no effect. It seems the treatment reduces mortality. p-value = 0.07 (not significant at alpha = 0.05)
B.Fail to reject H0; this data is consistent with the assumption that there is no effect. There is not enough evidence to conclude the treatment reduces mortality. p-value = 0.12 (not significant at alpha = 0.05)
C.Reject H0; this data is inconsistent with the assumption that there is no effect. It seems the treatment reduces mortality. p-value = 0.0007 (significant at alpha = 0.05)
D.Reject H0; this data is consistent with the assumption that there is no effect. It seems the treatment does not reduce mortality. p-value = 0.08 (not significant at alpha = 0.05)
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标准答案
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思路分析
We start by restating the scenario and the choices to ensure clarity of what’s being evaluated. Question setup: We compare mortality between two diet groups in 900 mice on a standard diet (p1 = mortality proportion) and 950 mice on a high-protein diet (p2 = mortality proportion). Observed data: 36 deaths in standard diet group, 15 deaths in high-protein group. H0: p1 = p2 (no difference in mortality between diets). H1: p1 > p2 (standard diet has higher mortality, i.e., the high-protein diet reduces mortality). Now we analyze each answer option one by one, noting what each claims and whether it matches the data and the stated hypotheses. Option A: “Fail to reject H0; this data is inconsistent with the assumption that there is no effect. It seems the treatment reduces mortality. p-value = 0.07 (not significant at alpha = 0.05)” - First, the claim that we fail to reject H0 conflicts with the observed large difference in mortality rates: 4.0% vs about 1.58%, which suggests evidence agains......Login to view full explanation

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