Preparing to Conduct a Chi-Square Test for Goodness of Fit — Quiz
Question 4 • Statistics
A prize wheel at a carnival consists of five equal sectors of these colors: red, blue, green, yellow, and orange. If the wheel lands on yellow, the player wins a prize. After observing several spins, a customer suspects that the wheel is not fair. To substantiate this belief, the customer observes 100 consecutive spins of the prize wheel. What are the appropriate hypotheses?
Answer
A
cap h sub 0 : The wheel is fair. cap h sub A : The wheel is not fair.
B
cap h sub 0 : The wheel will not land on red 20 times, blue 20 times, green 20 times, yellow 20 times, and orange 20 times. cap h sub A : The wheel will land on red 20 times, blue 20 times, green 20 times, yellow 20 times, and orange 20 times.
C
cap h sub 0 : The wheel is not fair. cap h sub A : The wheel is fair.
D
cap h sub 0 : The wheel will land on red 20 times, blue 20 times, green 20 times, yellow 20 times, and orange 20 times. cap h sub A : The wheel will not land on red 20 times, blue 20 times, green 20 times, yellow 20 times, and orange 20 times.
Explanation
The customer suspects the wheel is not fair, so that claim belongs in the alternative hypothesis: Hₐ: the wheel is not fair. The null hypothesis represents the no-change or fair condition: H₀: the wheel is fair, with each of the five colors equally likely. Fairness does not require exactly 20 occurrences of each color in 100 spins; random results can vary, so choices that state exact counts are not appropriate hypotheses.
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