From a collection of objects numbered { 1 , 2 , . . . . , K } objects are picked and replaced. We want to test H 0 : K = 100000 against H 1 &lt; 100000, with the highest ranking number M of our sample as test statistic. We find for our realisation for M the value 81115.What is the P value?The correct answer is: 0.015I know that the definition of the p-value is:The p-value is the probability of getting the observed value of the test static or a value with even greater evidence against H 0 , if the hypothesis is actually trueor in formula form P ( T ≥ t )I have the following questions:What are T and t?I think that distribution is uniform, but how do I calculate the p-value?

Question

From a collection of objects numbered   {  1  ,  2  ,  .  .  .  .  ,  K  } objects are picked and replaced. We want to test       H    0    :  K  =  100000 against       H    1    &amp;lt;  100000, with the highest ranking number   M of our sample as test statistic. We find for our realisation for   M the value   81115.What is the   P value?The correct answer is:   0.015I know that the definition of the   p-value is:The p-value is the probability of getting the observed value of the test static or a value with even greater evidence against       H    0  , if the hypothesis is actually trueor in formula form   P  (  T  ≥  t  )I have the following questions:What are   T and   t?I think that distribution is uniform, but how do I calculate the   p-value?

mar1nerne · Accepted Answer

In a uniform distribution defined between the values   a and   b, the cdf for   k    ϵ    [  a  ,  b  ] is   (  k  −  a  )  /  (  b  −  a  ).

Dale Tate · Accepted Answer

The probability that one randomly chosen object is at most   81115 is   q  =  81115  /  100000. Since the draws are independent (because they are replaced after each pick), the probability that all   20 choices are less than or equal to 81115 is   p  =      q      20    =  0.015..

From a collection of objects numbered { 1 , 2 , . . . ....

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