Final answer:
The upper limit of the 80% confidence interval is found by adding the margin of error to the sample proportion. Using the formula, it calculates to approximately 74.6%.
Explanation:
In statistical analysis, a confidence interval is a tool that quantifies the uncertainty associated with estimating a population parameter from a sample. For this specific scenario, where the University conducted a survey on housing options for first-year students, an 80% confidence interval was chosen. The upper limit of this interval, denoting the maximum likely proportion of students in favor of increasing housing options, is calculated by adding the margin of error to the sample proportion.
The margin of error is influenced by the confidence level and the standard error of the sample proportion. In this case, the 80% confidence level corresponds to a z-score, a statistical measure reflecting the number of standard deviations a data point is from the mean. Using the z-score for the upper tail of the distribution, the margin of error is determined and added to the sample proportion. This process encapsulates the inherent variability in estimating population parameters based on a finite sample.
In essence, the upper limit serves as a boundary within which we can reasonably expect the true proportion of students supporting increased housing options to lie, given the statistical properties of the sample. This method provides a practical and mathematically grounded approach to express the precision of survey results in the broader context of the entire student population.