john runs an experiment with an alpha of 0.05. he is able to reject the null. john then runs a second experiment with an alpha of .05. assume that the null hypothesis was correct both times... what probability theorem would we use to calculate the probability of incorrectly rejecting the null hypothesis twice in a row?

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20-12-2022
Mathematics

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john runs an experiment with an alpha of 0.05. he is able to reject the null. john then runs a second experiment with an alpha of .05. assume that the null hypothesis was correct both times... what probability theorem would we use to calculate the probability of incorrectly rejecting the null hypothesis twice in a row?

Answer :

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-25T11:29:21-05:00

Multiplication Theorem of Probability would be used to calculate the probability of incorrectly rejecting the null hypothesis twice in a row

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

What exactly is the probability multiplication theorem ? The probability of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

Explanation:

Alpha was set to 0.05. This means that for each experiment there is a .05 probability of incorrectly rejecting the null hypothesis (when the null is true). John rejected the null hypothesis incorrectly twice in a row. The probability of doing this on the first experiment was .05. The probability of doing this on the second experiment was .05. The probability of incorrectly rejecting the null on the first experiment AND the second experiment is calculated using the Multiplication Theorem of Probability. p(reject null on 1st experiment AND reject null on 2nd experiment) =p(reject null on 1st experiment) x p(reject null on 2nd experiment)

The multiplication theorem is: p(A and B) = p(A) * p(B).

Hence Multiplication Theorem of Probability would be used to calculate the probability of incorrectly rejecting the null hypothesis twice in a row.

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