There Is an Option of Paying $100 to Have Research

question 27

Multiple Choice

There is an option of paying $100 to have research done to better predict which state of nature will occur.When the true state of nature is S1,the research will accurately predict S1 60% of the time.When the true state of nature is S2,the research will accurately predict S2 80% of the time.
-Given that the research is done,what is the joint probability that the state of nature is S2 and the research predicts S2?

• A)0 08
• B)0 16
• C)0 24
• D)0 32
• E)0 36

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Definitions:

Chi-squared Test

A statistical test used to determine if there is a significant difference between observed frequencies and expected frequencies in categorical datasets.

Chi-squared Distribution

A statistical distribution that is used primarily in hypothesis testing and is derived from the sum of squared standard normal deviates.

Proportion

A statistical measure that indicates the fraction of the total number of items in a certain category or characteristic.

Two-tail Test

A statistical test that is used to determine if there is a significant difference between a sample and a particular population mean, where the critical region is split between both tails of the distribution.