Hypothesis Test Question

• Jan 23rd 2009, 11:50 AM
flaming
Hypothesis 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 PM
Rapha
Quote:

Originally Posted by flaming
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.

I don't know. But I guess it's kinda helpful knowing what the probability is.

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

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 AM
mr fantastic
Quote:

Originally Posted by Rapha
I don't know. But I guess it's kinda helpful knowing what the probability is.

=> $\displaystyle \begin{pmatrix} 10 \\ 3 \end{pmatrix}$
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") = $\displaystyle \begin{pmatrix} 10 \\ 3 \end{pmatrix}*0.2^3*0.8^7 \approx 0.20$
Since the null hypothesis is student is guessing I think you'll actually need to calculate $\displaystyle \Pr(X \leq 3)$.