University officials say that at least 70% of the voting student population supports a fee increase. If the 95% confidence interval estimating the proportion of students supporting the fee increase is [0.75, 0.85], what conclusion can be drawn?
A)70% is not in the interval, so another sample is needed.
B)70% is not in the interval, so assume it will not be supported.
C)The interval estimate is above 70%, so infer that it will be supported.
D)Since this was not based on population, we cannot make a conclusion.

Question

Quizplus · Accepted Answer

The 95% confidence interval estimate provides a range within which the true proportion of students supporting the fee increase is likely to fall. Since the upper limit of the interval is 0.85, which is higher than the known value of 70%, we can infer that it is likely that the fee increase will be supported by the students. Option C correctly reflects this inference. Option A is incorrect because obtaining another sample is not necessary, as the interval already provides an estimate of the true proportion. Option B is incorrect because it assumes that 70% will not be supported, which cannot be concluded from the given information. Option D is incorrect because the inference is made based on the sample, but the estimate is expected to generalize to the population.

University Officials Say That at Least 70% of the Voting