作者libitum (libitum)
看板Statistics
标题[问题] 一题两独立母体比例差的假说检定
时间Mon May 11 10:54:03 2020
想请教遇到的一题问题，题目如下
In one country, 52% of the population are males, and 48% are female.
In another country, 47% are male, and 53% are females.
Suppose that a random sample of 100 people are picked from each country
(total number of observations: 200).
What is the probability that a sample of this size would be
able to reject the null hypothesis that the proportion of males
in the first population are greater than the second population
at an alpha level of 0.05?
(note: round this probability to two decimal places)
我的问题主要是在 the probability of rejecting the null hypothesis?
不是根据alpha value去决定那个机率是否reject null hypothesis吗
但感觉又没有那麽简单...
谢谢
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1F：→ andrew43: 应该是要你算power的意思 05/11 11:07
2F：→ libitum: 我来试试看 谢谢 05/11 11:32
想确认一下
power is the probability of rejecting H0 when H0 is false
所以
p1 = the probability of male shows in the first group (0.52)
p2 = the probaiblity of male shows in the second group (0.47)
H0: p1 <= p2
H1: P1 > p2
是这样吗 谢谢
※ 编辑: libitum (72.88.166.22 美国), 05/11/2020 11:53:41
3F：→ andrew43: 就是算实际上p=0.47的抽样分配可拒绝不正确的H0:p=0.52 05/11 18:47
4F：→ yhliu: 是在 p1=0.52, p2=0.47 的情况下计算 reject H0 的机率. 05/11 18:53
5F：→ yhliu: "Reject H0" 是在问题所定显着水准下所决定的事件. 05/11 18:55
6F：→ andrew43: 抱歉说错。谢谢老师。H0应该是p1-p2<=0，且应关心p1-p2 05/11 19:06
7F：→ andrew43: 的抽样分配。 05/11 19:06
8F：→ andrew43: 解题应该就从比较两样本比例的检验查起。 05/11 19:10
9F：→ andrew43: 常见教材应该会写到以CLT近似的解法。 05/11 19:13
10F：→ andrew43: 更正 H0 p1-p2 gt 0 05/11 19:45
11F：→ libitum: H0:p1-p2 >= 0 ? 05/12 04:46
12F：→ libitum: 所以要算Pr(p1-p2<0)? 05/12 04:47
13F：→ yhliu: H1 是 p1 > p2, H0 是 p1=p2 或 p1≦p2. 在 p1=p2 之下根据 05/12 06:43
14F：→ yhliu: 显着水准 0.05 决定 reject H0 的规则, 然後在 p1=0.52, 05/12 06:46
15F：→ yhliu: p2 = 0.47 之下计算 reject H0 这一规则成立的机率. 05/12 06:47