A multiple-choice quiz contains ten questions. For each questions there are one correct answer and four incorrect answers. A student gets three correct answers on the quiz. Test the hypothesis that the student is guessing.

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- Jan 23rd 2009, 11:50 AMflamingHypothesis Test Question
A multiple-choice quiz contains ten questions. For each questions there are one correct answer and four incorrect answers. A student gets three correct answers on the quiz. Test the hypothesis that the student is guessing.

- Jan 23rd 2009, 06:45 PMRapha
I don't know. But I guess it's kinda helpful knowing what the probability is.

10 questions, 3 (questions correct answered) correct answers

=> $\displaystyle \begin{pmatrix} 10 \\ 3 \end{pmatrix}$

5 choices per question;

probability for guessing the right answer is therefor $\displaystyle \frac{1}{5} = 0.2;$

probability for guessing the wrong answer is therefor $\displaystyle \frac{4}{5} = 0.8.$

=> probability("three right answers") = $\displaystyle \begin{pmatrix} 10 \\ 3 \end{pmatrix}*0.2^3*0.8^7 \approx 0.20$

the probability of guessing exactly 3 correct answers out of 10 is 20% (=0.2) - Jan 24th 2009, 02:11 AMmr fantastic