Final answer:
The statement is true; a 95% confidence interval means that 95 out of 100 such intervals from repeated sampling would contain the true population proportion.
Step-by-step explanation:
True or False: There is a 95% probability that the confidence interval produced from this sample contains the proportion of all homeowners in Ypsilanti that support Proposal 127. This statement is True if the confidence interval was constructed correctly using the appropriate methods and formulae. A confidence interval is an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. If the confidence interval is said to be 95%, it means that if we were to take 100 different samples and compute a confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true population parameter.
For example, a confidence interval of 95% implies that we are 95% confident that the calculated interval contains the true proportion of the population that supports Proposal 127. This does not mean that there is a 95% probability that any given interval contains the true population proportion, but rather that 95% of intervals constructed from repeated random sampling of the population will contain the true proportion.
When interpreting a confidence interval, it's important to understand that the level of confidence is a reflection of the method used to estimate the interval, not a statement about a specific interval. The interpretation of a 90% confidence interval would be analogous; we would expect that if we took many samples and built a confidence interval for each one, about 90% of those intervals would contain the true population proportion. Similarly, constructing a confidence interval using the plus-four method for a proportion, such as with the poll about the likelihood of an event suggests that if the process is repeated multiple times, the specified percentage of those confidence intervals will contain the true population proportion or mean as indicated by the method's confidence level.