From a collection of objects numbered <mo fence="false" stretchy="false">{ 1 , 2 , .

Kassandra Ross 2022-06-20 Answered
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 < 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: 0.015
I 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 true
or 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?
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Answers (2)

mar1nerne
Answered 2022-06-21 Author has 20 answers
In a uniform distribution defined between the values a and b, the cdf for k ϵ [ a , b ] is ( k a ) / ( b a ).

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Dale Tate
Answered 2022-06-22 Author has 5 answers
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..

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