A teacher claims that on any given day, 60 percent of her students complete their homework and 40 percent do not. To investigate this belief, she randomly selects 30 of her 120 students and determines how many of them completed their homework that day and how many did not. She would like to know if her findings provide convincing evidence that the distribution of homework completion status differs from her original belief. Are the conditions for inference met?
Answer
A
Yes, all of the conditions for inference are met.
B
No, the 10 percent condition is not met.
C
No, the random condition is not met.
D
No, the Large Counts condition is not met.
Explanation
The sample is random, and the expected counts under the teacher’s claim are 30 × 0.60 = 18 students who complete homework and 30 × 0.40 = 12 who do not, so the Large Counts condition is met. However, the sample of 30 is 25% of the teacher’s 120 students, which is greater than 10%. Therefore, the 10 percent condition is not met, so the conditions for inference are not all satisfied.
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