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

question 7

True/False

A psychology instructor gave a five-question true-false quiz to her class of 201 students. The results were as follows.

$$\begin{array} { l | c c c c c c } \text { Number Correct } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 10 & 40 & 56 & 64 & 25 & 6\end{array}$$

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:

VFD

A Variable Frequency Drive is a motor controller device that operates an electric motor by adjusting the voltage and frequency provided to it.

Rectifier

An electrical device that converts alternating current (AC) to direct current (DC), allowing the flow of charge in one direction only.

Variable Torque

Refers to motors or drives designed to manage varying load torque demands in applications like fans or pumps.

Mechanical Loads

Forces, torques, or loads applied to a mechanical system, influencing its performance and structural integrity.