Determine Probability of Fourth Good Response After Three Successes

Q: Determine Probability of Fourth Good Response After Three Successes

This question evaluates understanding of Bernoulli trials and independence along with proficiency in comparative hypothesis testing for proportions, relevant to the Statistics & Math domain and typical for a Data Scientist role.

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Question

Evaluating Good-Response Rates for Chatbot Outputs

Context

You are evaluating chatbot/LLM responses. Treat each response as a Bernoulli trial (good vs not good). Unless otherwise noted, assume independence across responses.

Questions

If the probability any response is good is x, and the first three responses were good, what is the probability the fourth response will be good?
Model A shows 70% good responses and Model B shows 80% good responses, based on n1 and n2 evaluated responses, respectively. Using a two-proportion z-test at a 5% significance level:
- Test whether the difference is statistically significant.
- Report the test statistic and p-value.
- If n1 and n2 are not provided, show the general formula and then illustrate with an example (e.g., n1 = n2 = 100).

Determine Probability of Fourth Good Response After Three Successes

Evaluating Good-Response Rates for Chatbot Outputs

Context

Questions

Solution

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