A school principal claims the graduation rate at a school is 96%. Molly, a student at this school, takes a random sample of students and finds the 95% confidence interval for the true proportion of students graduating from this school is (0.934, 0.983). Is it reasonable to conclude the principal’s claim is incorrect?
Answer
A
No, because the interval contains 0.96.
B
No, because the interval contains values greater than 0.96.
C
Yes, because the interval has values less than 0.96.
D
Yes, because a different sample might give different results.
Explanation
The 95% confidence interval is (0.934, 0.983), and the claimed graduation rate of 0.96 lies inside it. Thus, 96% is a plausible value for the true graduation rate based on this sample, so there is not enough evidence to conclude that the principal’s claim is incorrect. The correct choice is “No, because the interval contains 0.96.”
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