题目
A bag contains a large number of marbles, each of which is blue or red.
A random sample of 3 marbles is taken from the bag.
The random variable represents the number of blue marbles taken minus the number of red marbles taken.
Given that 20% of the marbles in the bag are blue,
(a) show that P() = 0.384
(b) find the sampling distribution of
(c) write down the mode of
Takashi claims that the true proportion of blue marbles is greater than 20% and tests his claim by selecting a random sample of 12 marbles from the bag.
(d) Find the critical region for this test at the 10% level of significance.
(e) State the actual significance level of this test.
题目中文翻译
一个袋子里有大量弹珠，每个弹珠要么是蓝色，要么是红色。
从袋中随机取出 3 个弹珠组成样本。
随机变量 表示取出的蓝色弹珠数量减去取出的红色弹珠数量。
已知袋中 20% 的弹珠是蓝色。
(a) 证明 。
(b) 求 的抽样分布。
(c) 写出 的众数。
Takashi 认为蓝色弹珠的真实比例大于 20%，并通过从袋中随机抽取 12 个弹珠来检验他的说法。
(d) 求该检验在 10% 显著性水平下的临界域。
(e) 写出该检验的实际显著性水平。