Final answer:
The survey finding that 51% of US adults know their neighbors suggests over half do, but a confidence interval calculation is needed to make a definitive statement. By constructing a confidence interval and checking if its lower bound exceeds 50%, we could determine this with a certain level of confidence.
Step-by-step explanation:
A survey of 2255 randomly selected US adults found that 51% said they know all or most of their neighbors. To determine whether this provides evidence that more than half of US adults know most or all of their neighbors, we can look at the confidence interval for the proportion.
Typically, a confidence interval is constructed to estimate the true population proportion with a certain level of confidence, say 95%. The sample proportion is used as the point estimate, and the error bound is calculated based on the desired confidence level and sample size. In this case, the point estimate is 51%. To determine whether we can be confident that more than half of the adults really do know their neighbors, we would calculate the lower bound of the confidence interval. If this lower bound is above 50%, then we have evidence to suggest that more than half of the US adults know most or all of their neighbors, at the given level of confidence.
It's analogous to how the market research firm determined the confidence interval for the proportion of adults with cell phones, or how the broker verified the accuracy of a survey about family stock ownership at a certain significance level, as in examples provided.