Question

In: Statistics and Probability

Does a student just guess on a multiple-choice test or do they actually understand the material?...

Does a student just guess on a multiple-choice test or do they actually understand the material? An instructor gives an exam that consists of 100 multiple-choice questions. Each question has four possible answers. The student in question completes all 100 questions. The result is that the student has 31 of the answers correct. Does this provide sufficient evidence to rule out random guessing by the other student? Conduct an appropriate test of hypothesis, providing assumptions, hypothesis, test statistic, p-value, and conclusion.

Solutions

Expert Solution

If student just guess on a multiple-choice test then the expected number of questions answered correctly will be =

= (1/4)*100 = 25

Now, we conduct the Z-test for one population proportion as :

Hence, there is not enough evidence to conclude that student actually understand the material at 5 % level of significance.

orchestra answered 2 years ago
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