A Psychology Instructor Gave a Five-Question True-False Quiz to Her

question 26

Short Answer

A psychology instructor gave a five-question true-false quiz to her class of 193 students. The results were as follows.

$$\begin{array} { l | c c c c c c } \text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 6 & 26 & 58 & 59 & 25 & 19\end{array}$$

The instructor thinks that the students may have answered the questions by guessing, so that the probability that any given answer is correct is 0.5. Under the null hypothesis, the number of correct answers has a binomial distribution with 5 trials and success probability 0.5.
Perform a chi-square test of this hypothesis. Can you reject H₀ at the $\alpha$ =0.01 level?

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Definitions:

Fluid Intelligence

The ability to reason and solve new problems independently of previously acquired knowledge.

Crystallized Intelligence

The ability to use learned knowledge and experience, which typically increases or remains stable over the lifespan.

Diverge

To move or extend in different directions from a common point, or to differ in opinion or character.

Converge

To move towards one point from different places or ideas; to come together and meet or unite in a point or purpose.