A survey of an urban university (population of 25,450) showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. If university officials say that at least 70% of the voting student population support the fee increase, what conclusion can be drawn based on a 95% level of confidence?
A) 70% is not in the interval, need to take another sample.
B) 70% is not in the interval, so assume it will not be supported.
C) 70% is below the interval, so assume it will be supported.
D) Since this was not based on population, cannot make conclusion.

Question

Quizplus · Accepted Answer

The proportion of sampled students who support the fee increase is 870/1100 = 0.79 or 79%. To determine if the actual support level in the population is at least 70%, we can calculate a confidence interval around the sample proportion. Without doing the exact math, if we're working with a 95% confidence level, the interval would typically be narrower than the 9% difference between the sample proportion and the 70% threshold, suggesting that the true population proportion supporting the fee increase is likely above 70%. Thus, it's reasonable to conclude that the support will be there, making option C the correct choice.

A Survey of an Urban University (Population of 25,450) Showed