Final answer:
The truth of the statement depends on the outcome of statistical analysis like confidence interval overlap or hypothesis testing. If the confidence intervals overlap or no significant difference is found, the statement is true; otherwise, it is false.
Step-by-step explanation:
The statement 'statistically, we cannot conclude that the proportions of people who do and do not feel safe walking in their neighborhood at night are unequal' could be true or false depending on the context and the statistical analysis performed.
If the confidence intervals for the proportions overlap, or if a hypothesis test results in a p-value higher than the chosen significance level (usually 0.05), we would not reject the null hypothesis that the proportions are equal, and the statement would be true.
On the other hand, if the confidence intervals do not overlap and/or if the hypothesis test gives a p-value lower than the significance level, indicating that the observed difference is statistically significant, then the statement would be false.
For example, consider a scenario where the confidence intervals of the proportion of people who feel safe are (0.65, 0.76) and the proportion of those who do not feel safe are (0.60, 0.72). These intervals overlap, suggesting there isn't a significant difference between the two proportions.
In such a case, maintaining that we cannot conclude the proportions are unequal would be correct. However, if the intervals are (0.72, 0.82) for those who feel safe and (0.50, 0.60) for those who do not, then they do not overlap, indicating a statistically significant difference. In this case, saying that we cannot conclude that the proportions are unequal would be incorrect.