使用t检验进行统计中的假设检验 [英] hypotheses test in statistics using t-test
问题描述
t检验:配对两个均值样本
t-Test: Paired Two Sample for Means
sold price dummy
Mean 591.857 0
Variance 72542.476 0
Observations 7 7
Pearson Correlation #DIV/0!
Hypothesized Mean Difference 700
df 6
t Stat -1.0623
P(T<=t) one-tail 0.1645
t Critical one-tail 1.9432
P(T<=t) two-tail 0.3290
t Critical two-tail 2.4469
你能帮我回答这些问题吗?
(a)以符号形式写出原假设和替代假设.
(b)这是单尾还是双尾测试?
(c)使用p值方法，说明您为什么拒绝否定假设.
(d)在此假设检验中，在变量的上下文中做出简短的统计结论.
can u help me to answer these questions
(a) Write, in symbolic form, the null and alternative hypotheses.
(b) Is this a one-tailed or two-tailed test?
(c) Using the p-value approach, state why you would reject the null hypothesis or not.
(d) Make a brief statistical conclusion in the context of the variable in this hypothesis test.
推荐答案
您提出的第一个问题:
(a)以符号形式写出原假设和替代假设."
不能从一组统计信息中得出.
看一下此链接:
http://en.wikipedia.org/wiki/Null_hypothesis [ http://en.wikipedia.org/wiki/Statistical_hypothesis_testing [ http://en.wikipedia.org/wiki/Student''s_t-test [ ^ ]
从关于假设检验的文章开始-它似乎是最简单，最易接近的.然后查看有关零假设的文章，然后处理学生的T检验文章.
在阅读它们时，每当您进入一个不理解的部分时，请确保您对该部分有很好的了解，然后再进入下一个部分.麻烦通常是您在此之前没有完全了解本节内容.通常最困难的是所有术语-如果您不确定某个词或术语，则可以在文本中查找它，或在google中搜索它，或类似的东西以便对它有一个很好的定义.您可能会发现，在真正理解您最初阅读的内容之前，需要花费数小时的时间在单词定义中查找单词，但是缺少让别人用您能够理解的语言向您解释的内容，这是唯一的方法您将了解它.最后，值得理解它，因为您可以在将来的工作中使用它作为工具.
The first question that you ask:
"(a) Write, in symbolic form, the null and alternate hypotheses."
is not something that can be derived from a set of statistics.
Take a look at this link:
http://en.wikipedia.org/wiki/Null_hypothesis[^]
This is also a good reference:
http://en.wikipedia.org/wiki/Statistical_hypothesis_testing[^]
Statistics are not used to derive a hypothesis.
Statistic are used to determine the probability that a given hypothesis is true or false.
The fact that you are asking us to provide you an answer to (a) without providing us enough information to do so, suggests that there is something very fundamental that you don''t understand about the issue of statistics.
It would do you no good for us to provide you an answer that you don''t actually understand.
I suggest you review the two links above as well as:
http://en.wikipedia.org/wiki/Student''s_t-test[^]
Start with the article on hypothesis testing -- it seems to be the simplest and most approachable. Then look at the article on Null Hypothesis, and then tackle the Student''s T-test article.
As you read them, whenever you come to a section you don''t understand, make sure you get a good grasp on that section before going to the next. Often the trouble will be you didn''t quite get the section before that. Usually the hardest thing is all the terminology -- if there is a word or term that you aren''t sure of, then look it up in your text, or google it, or something so that you get a good definition of it. You might find it takes hours of looking up words within definitions of words before you actually understand what the heck you were originally reading, but short of having somebody explain it to you in language that you do understand, that''s about the only way you are going to understand it. In the end, it''s worth the work of understanding it because then you can use that as a tool in future work you do.
我假设您有一个7号样本，假设这些值是固定价格零(您的虚拟商品)的售价.您得到的平均值为591.9，大"标准偏差为269.3，这是72542.5的平方根.您的个人价值可能会大于700，而有些会小于700，但所有价值都以591.9为中心.一目了然，样本均值(= 591.9)可能会让您认为该人群的售价低于700.使用假设检验.
因此，现在您想使用您的样本结果来得出人口的推论，该人口的销售价格(i)不等于700 ，或(ii)大于700，或(iii)小于700.
从您的结果中，我可以看到您正在使用配对t检验.
巧合的是，我已经开发了一些用于上述目的的Excel Stat工具.以下是我从使用Excel Stat工具获得的结果.它回答了您的问题(a)至(d).
I assume you have a sample of size 7 and assume those values are sold prices from a fixed value, zero(your dummy). You get an average of 591.9 with a "big" standard deviation of 269.3, which is the square root of 72542.5. You may have some individual value more than 700 and some less than 700, but all centering at 591.9. At a glance, sample mean (=591.9) may make you think that the population may have sold price less than 700. But you want to conclude in a more objective way, e.g. using hypothesis testing.
So now you want to use your sample results to draw an inference about the population that the population has sold price (i) not equal to 700, or (ii) more than 700, or (iii) less than 700.
From your results, I can see that you are using paired t test.
Coincidentally, I have developed some Excel Stat tool that serve the above purpose. Following is the result i get from using the Excel Stat tool. It answers your question (a) to (d).
Two-Samples Paired t-Test
Sample Size = 7
Average Difference= 591.857
Stdev. of Difference= 269.3371
Significance Level(alpha)= 0.05
Hypothesized Difference = 700
Test Statistics -1.0623
H0 : µ1-µ2 = 700 H0 : µ1-µ2 >= 700 H0 : µ1-µ2 <= 700
H1 : µ1-µ2 != 700 H1 : µ1-µ2 < 700 H1 : µ1-µ2 > 700
or or or
H0 : µD = 700 H0 : µD >= 700 H0 : µD <= 700
H1 : µD != 700 H1 : µD < 700 H1 : µD > 700
2-Tailed 1-Tailed Left 1-Tailed Right
Critical t Value ±2.4469 -1.943180281 1.943180281
p-value 0.3290 0.1645 0.8355
Conclusion Not Reject H Null Not Reject H Null Not Reject H Null
有3列.左列不等于700，中间列小于700，右列大于700.
对于您的问题(a)，可以用3种方式显示，即不等于700，小于700和大于700.µ1是售价的平均值，µ2是虚拟价格的平均值，µD是平均值差异.
对于问题(b-d)，这取决于您对什么进行测试.再一次，我假设您想证明人口的出售价格小于700 (单尾检验，请参见中间栏).您的结果表明您使用的alpha为0.05.
使用p值，它是0.1645，大于0.05，因此得出的结论是:不拒绝H null，这意味着不拒绝出售价格= 700.推论是:人口出售价格不少于700 (但我们敢"不说出售价格是700或更高，因为不拒绝无效假设是弱"陈述).
使用t值，拒绝区域小于-1.943，并且您的t stat为-1.0623，它不属于拒绝区域，因此不会拒绝H null.
可悲的是，虽然你不能说出售价格低于700，但你没有强有力的证据表明出售价格是700假设检验是好"的拒绝，而不是相反.发生这种情况是因为标准偏差值很大.
另一种方法.您还可以进行一样本t检验.请参阅以下Excel结果.
There are 3 columns. Left column for not equal to 700, middle column for less than 700, and right column for more than 700.
For your question (a), it can be shown in 3 ways namely, not equal to 700, less than 700, and more than 700. µ1 is the mean of sold price, µ2 is the mean of dummy, and µD is the mean of differences.
For question (b - d), it depends on what do you test on. Again I assume you want to show that sold price of population is less than 700 (one-tailed test, see middle column). Your results show that alpha you use is 0.05.
Using p-value, it is 0.1645 which is more than 0.05, so conclusion is: Not reject H null, that means Not reject sold price =700. Inference is: population sold price is not less than 700 (but we "dare" not say sold price is 700 or more, because not rejecting null hypothesis is a "weak" statement).
Using t value, reject area is less than -1.943, and your t stat is -1.0623 which is not fall in reject area, thus not reject H null.
Sad to say that although you cannot say sold price is less than 700, but you do not have strong evidence showing that sold price is 700. Hypothesis testing is "good" for rejecting, not the opposite. This happen due to the big value of standard deviation.
Another method. You can also conduct a one-sample t test. See the following Excel results.
One-Sample t-Test
Hypothesized miu = 700
Sample size = 7
Sample Mean = 591.857
Sample Stdev.= 269.3371
Significance Level = 0.05
Test Statistics = -1.06
H0 : µ =700 H0 : µ >=700 H0 : µ <=700
H1 : µ !=700 H1 : µ < 700 H1 : µ > 700
2-Tailed 1-Tailed Left 1-Tailed Right
Critical t Value ±2.4469 -1.9432 1.9432
p-value 0.3290 0.1645 0.8355
Conclusion Not Reject H Null Not Reject H Null Not Reject H Null
您将得到类似的结论
您可以转到下面的链接以获得用于上述目的的Excel加载项工具的副本.
http://www.foundasoft.com/index.php?option=com_wrapper& view = wrapper& Itemid = 94 [ ^ ]
http://www.foundasoft.com/index.php? option = com_content& view = article& id = 84& Itemid = 90 [
You will get similar conclusions
You can go to below link to get a copy of Excel add-in tool for above purpose.
http://www.foundasoft.com/index.php?option=com_wrapper&view=wrapper&Itemid=94[^]
http://www.foundasoft.com/index.php?option=com_content&view=article&id=84&Itemid=90[^]
Hope this help.
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