CSIR NET Mathematics 2024|Testing of Hypothesis | 21 February 2024

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 :

In order to test the randomness of a series of observations the appropriate non- parametric test is

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

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

Let  denote a random sample from normal distribution with mean zero and variance . The region

Where  is chosen so that the test has  level of significance, is a uniformly most powerful region for testing  against  when