Preparing to Conduct a Chi-Square Test for Goodness of Fit — Quiz
Question 9 • Statistics
Students at a large university have four places to get lunch: the cafeteria, the hut, the taco wagon, or the pizza place. An article in the school newsletter states that 70 percent of students prefer to get lunch in the cafeteria and the other three options are preferred equally. To investigate this claim, a random sample of 150 students is selected. What are the appropriate hypotheses?
Answer
A
cap h sub 0 : The distribution of lunch preferences is 70 percent cafeteria, 10 percent hut, 10 percent taco wagon, and 10 percent pizza place. cap h sub A : The distribution of lunch preferences is not 70 percent cafeteria, 10 percent hut, 10 percent taco wagon, and 10 percent pizza place.
B
cap h sub 0 : In the sample of 150 students, the distribution will not be that 105 will prefer the cafeteria, 15 will prefer the hut, 15 will prefer the taco wagon, and 15 will prefer the pizza place. cap h sub A : In the sample of 150 students, 105 will prefer the cafeteria, 15 will prefer the hut, 15 will prefer the taco wagon, and 15 will prefer the pizza place.
C
cap h sub 0 : In the sample of 150 students, 105 will prefer the cafeteria, 15 will prefer the hut, 15 will prefer the taco wagon, and 15 will prefer pizza place. cap h sub A : In the sample of 150 students, the distribution will not be that 105 will prefer the cafeteria, 15 will prefer the hut, 15 will prefer the taco wagon, and 15 will prefer the pizza place.
D
cap h sub 0 : The distribution of lunch preferences is not 70 percent cafeteria, 10 percent hut, 10 percent taco wagon, and 10 percent pizza place. cap h sub A : The distribution of lunch preferences is 70 percent cafeteria, 10 percent hut, 10 percent taco wagon, and 10 percent pizza place.
Explanation
The claim describes the distribution of preferences in the student population: 70% prefer the cafeteria, and the remaining 30% is split equally, or 10% for each other place. The null hypothesis states this claimed distribution, and the alternative says the distribution is different. Therefore, choice A is correct; hypotheses should describe population proportions, not exact counts in this particular sample.
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