University-数学讨论区-Probability and Statistic I, II

dunwan2tellu

原帖由 mad1427 于 21-10-2007 10:10 PM 发表
请问什么是anova呢。。。？

Analysis of Variance (ANOVA)

用途：to test the hypothesis that the means among 2 or more groups are equal, (assumption :sampled populations 必须 normally distributed)

和 F-test 概念一样都是用 variance 来 test ,不过 ANOVA 可以 test >2 group data , F-test 只有 2 个。

[ 本帖最后由 dunwan2tellu 于 21-10-2007 11:03 PM 编辑 ]

mad1427

谢谢,那f-test又是什么呢...?

zhaoqi

原帖由 dunwan2tellu 于 21-10-2007 10:59 PM 发表


Analysis of Variance (ANOVA)

用途：to test the hypothesis that the means among 2 or more groups are equal, (assumption :sampled populations 必须 normally distributed)

和 F-test 概念一样 ...

也可以从F-test里看到该reject或accept hypothesis吧？

dunwan2tellu

原帖由 mad1427 于 22-10-2007 08:32 AM 发表
谢谢,那f-test又是什么呢...?

F-Test : Test 2 group of data's difference in sample variance

原帖由 zhaoqi 于 22-10-2007 09:05 AM 发表


也可以从F-test里看到该reject或accept hypothesis吧？

当然 ,hypothesis test 的目的本就如此

gsan

不是很会做那个(n x)的东东.有谁能帮帮我?

[ 本帖最后由 gsan 于 1-11-2007 11:02 AM 编辑 ]

gsan

原帖由 dunwan2tellu 于 26-9-2007 01:58 PM 发表


T-test(T-distribution) and Z-test(normal distribution) is a test which compare the difference between the mean of two groups of data.

F-test (F distribution) : A test to compare the varia ...

怎样分别Z和T-test呢?在T-test里面,又怎样分别variance equal or not equal or paired test的case呢?

[ 本帖最后由 gsan 于 1-11-2007 02:32 PM 编辑 ]

gsan

谁能告诉我答案?我有一点的confuse啊

gsan

In a code size comparison study, five determinations of the number ofbytes required to code 5 workloads on two different processors wererecorded. The data are given below:

system 1: 101, 144, 211, 288, 72
system 2: 130, 180, 141, 374, 302

Do the data indicate a significant difference between the two systems? Assume that the data comes from a normal distribution.

我可以直接用paired t-test来solve吗?

zhaoqi

问题一：
An urn contains b black balls and r red balls.
One of the ball is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with it.
Now suppose that we draw another ball.
What is the probability that the first ball drawn was black given that the second ball drawn was red?

问题二：
A bowl contains w white balls and b black balls.
A ball is selected at random from the bowl, its color is noted and then returned to the bowl along with n additional balls of the same color.
Another ball is randomly selected from the bowl and its observed that the  ball is black,
What is the probability that first ball selected was white?

来研究一下，这两题的问答方式是否用一样的原理来解答？

问题一： P(B|R)?
问题二： P(W|B)?

flash

原帖由 zhaoqi 于 16-1-2008 02:06 PM 发表
问题一：
An urn contains b black balls and r red balls.
One of the ball is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with it.
Now suppose t ...

对，两题的做法都是大同小异。。。。。

白羊座aries

那麽這題如何

A fair dice is tossed.If the number obtained is a multiple of 3,a marble will be drawn at random from bag A which contains 10marbles of which x are white marble.If the number obtained when tossing the dice is not a multiple of 3,a marble is drawn from bag B which also contains 10marbles of which y are white marbles.Given that the probability of obtaining a white marble in the above event is 1/2


when the marbles from bag A and bag B are put into a box,and two marbles are drawn at random from the box,the probabilityof obtaining two white marbles is 18/95.Find the values of x and y.

flash

原帖由 白羊座aries 于 31-1-2008 04:06 PM 发表
那麽這題如何

A fair dice is tossed.If the number obtained is a multiple of 3,a marble will be drawn at random from bag A which contains 10marbles of which x are white marble.If the number obtained  ...

答案应该是
x = 3, y = 6

~HeBe~_@

来把~~我们来做做这题。。。
农历新年的题目。。。
xexe

Expand P(A U B U C U D)
in terms of unions and/or intersections of atl east 1 of the 4 sets

[ 本帖最后由 ~HeBe~_@ 于 3-2-2008 04:54 PM 编辑 ]

JamesTea

想问下其实我们要如何断定问题里面的 variance is known or unknown 的呢？？

我 assignment 里面有一题是酱问的：（full question 已经忘记了，我只好说重点）

A manufacturer wish to change his old machine in producing glass bottles. His old machine produces bottles at average of 150 bottles with standard deviation of 6 bottles. If the new machine is able to produce more bottles, then the manufacturer will make a change. A sample of 16 parallel runs taken from the process and the average of bottles pruduced by new machine is 153 bottles. What decision can the manufacturer make ?? Use 0.05 significant different.

其实我们应该用 t-dist. 是 normal dist. 呢 ？？我算到的答案最后是 non reject 。但是我不太清楚 variance 是 known 还是 unknown ？？因为只是给 population 的 standard deviation 而已,就连 null hypothesis 和 alternative hypothesis 是放什么我也不太清。所以我是用 t-dist. 来做的。以下是我的 procedures，请学长们帮帮忙检查看有错误吗 ？？

1) H_0 : the new machine will produce more bottles
2) H_1 : the new machine will not produce more bottles
3) alpha = 0.05
4) critical region :   since n<30 and variance unknown -> t-dist.
       df = 16 - 1 = 15
       alpha = 0.05
       t_0.05,15 = 9.488(如果没有记错)
       reject H_0 if t > t_0.05,15

5) computation:
       t = (X-m)/(var/sqrt n)
         = (153-150)/(6/sqrt 16)
         = 2 < t_0.05,15

6) Conclusion : do not reject H_0. The new machine will produce more bottles.


可是我再从新看了很久，都是觉得好像很怪那答案。。。。

dunwan2tellu

你的 H0 和 H1 倒翻了,应该是 (H0 通常表示没有变化）

Ho : u = 150
H1 : u > 150

在这里你知道 population standard deviation = 6 , （所谓的 true standard deviation)
所以你的 standard deviation of mean = 6/sqrt[16] = 1.5

如果你不知道 true variance 的话,就用 estimator ，s 来预测 他的 variance

注意这里是 one tail test . 我 check table 看到 T_0.05,15 = 1.753

[ 本帖最后由 dunwan2tellu 于 7-4-2008 09:56 AM 编辑 ]

JamesTea

原帖由 dunwan2tellu 于 7-4-2008 09:53 AM 发表
你的 H0 和 H1 倒翻了,应该是 (H0 通常表示没有变化）

Ho : u = 150
H1 : u > 150

在这里你知道 population standard deviation = 6 , （所谓的 true standard deviation)
所以你的 standard deviation of  ...

那 standard deviation 其实可以当做是 known variance 吗 ？？因为我朋友用 normal dist 的方法做，结果和你一样。。。

hamilan911

standard deviation 是true variance(known variance)的平方根，知道了true variance，所以不需要用s来estimate
用sigma或用s要看题目怎么问，通常都会很明显

n=16<30, 应该用t-dist

sushi-x

请问 chi-square 是 test variable independent to each other 还是dependent to each other?

dunwan2tellu

原帖由 sushi-x 于 9-4-2008 08:37 AM 发表
请问 chi-square 是 test variable independent to each other 还是dependent to each other?

任何 hypothesis testing 都是要 test variable independent 或 dependent to each other 的。

用 test  的 人的角度来看的话，是希望他们之间有关系 ,也就是 dependent to each other . 这只会发生当你 reject 你的 null hypothesis 时候。

但是那个 test 本身是没有任何观点说是要 test independent 或 dependent 的。

cold_spoon

我最近做着一些IQ test，里面有些Numerical reasoning的部分有点不明白，所以想请教你们。

1. A man has 53 socks in his drawer: 21 identical blue, 15 identical black and 17 identical red. The lights are fused and he is completely in the dark. How many socks must he take out to make 100 percent certain he has a pair of black socks?
答案是40。为什么？我给的答案是38，原因很简单，拿完蓝色和红色的出来，不久100%黑色了  不过如果问题那么容易的话就不叫IQ test了...

2. How many minutes is it before 12 noon if nine minutes ago it was twice as many minutes past 10am?
答案是37minutes，我看了解释还是不大明白为什么，所以想请教你们。

[ 本帖最后由 cold_spoon 于 17-4-2008 05:56 PM 编辑 ]