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Correct typesetting (previous resulted in an error which has now led to a clarifying question in another thread)
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edit approved Sep 3, 2020 at 7:53
Eric Perkerson
edit approved Sep 3, 2020 at 7:53
Eric Perkerson
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I came across a question that I have no clue how to answer:

Suppose you are designing a diagnostic multiple choice quiz with the goal of distinguishing learners who have mastered a concept (P(correct|mastery) >= 1/2)$(P(\text{correct}|\text{mastery}) \ge 1/2)$ from learners who are randomly guessing (P(correct|~mastery) = 1/4)$(P(\text{correct}|\text{~mastery}) = 1/4)$.

What is the minimum number of questions necessary to be able to declare that a learner has mastered a concept with at least 95% probability?

Assume statistical independence for the different questions, and P(mastery) = 1/2.

I came across a question that I have no clue how to answer:

Suppose you are designing a diagnostic multiple choice quiz with the goal of distinguishing learners who have mastered a concept (P(correct|mastery) >= 1/2) from learners who are randomly guessing (P(correct|~mastery) = 1/4).

What is the minimum number of questions necessary to be able to declare that a learner has mastered a concept with at least 95% probability?

Assume statistical independence for the different questions, and P(mastery) = 1/2.

I came across a question that I have no clue how to answer:

Suppose you are designing a diagnostic multiple choice quiz with the goal of distinguishing learners who have mastered a concept $(P(\text{correct}|\text{mastery}) \ge 1/2)$ from learners who are randomly guessing $(P(\text{correct}|\text{~mastery}) = 1/4)$.

What is the minimum number of questions necessary to be able to declare that a learner has mastered a concept with at least 95% probability?

Assume statistical independence for the different questions, and P(mastery) = 1/2.

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Shengjie Zhang
Shengjie Zhang
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How to determine sample size

I came across a question that I have no clue how to answer:

Suppose you are designing a diagnostic multiple choice quiz with the goal of distinguishing learners who have mastered a concept (P(correct|mastery) >= 1/2) from learners who are randomly guessing (P(correct|~mastery) = 1/4).

What is the minimum number of questions necessary to be able to declare that a learner has mastered a concept with at least 95% probability?

Assume statistical independence for the different questions, and P(mastery) = 1/2.