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CSIR NET Mathematics 2024|Testing of Hypothesis | 21 February 2024
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Question 1
Let X be distributed as
and let
,
. The best critical region based on X for testing the null hypothesis
against the alternative hypothesis
is given by
. If
, then the value of
is :
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293103496797.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293104283536.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293105047526.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293105796610.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293106547784.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293107307750.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293108061598.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293108793632.png)
Question 2
In order to test the randomness of a series of observations the appropriate non- parametric test is
Question 3
In order to test whether a coin is unbiased, it is tossed 4 times. The null hypothesis of unbiasedness is rejected if and only if more than 3 heads are obtained. Then the size of the test is
Question 4
While testing of hypothesis
against
on ethe basis of a random sample from normal distribution
, then
was rejected at
level of significance. The corresponding p – value is
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293123399732.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293124178836.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293124938975.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293125697598.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293126483467.png)
Question 5
Let
denote a random sample from normal distribution with mean zero and variance
. The region
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/1695293130278717.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ121842/169529313106733.png)
Where is chosen so that the test has
level of significance, is a uniformly most powerful region for testing
against
when
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Feb 21CSIR NET & SET