Question

a news article reports the results of a survey of columbus residents who were asked whether they support plans to build a large shopping mall in the center of the city. the article states that a 95% confidence interval for the proportion who support the plan is 0.42 ± 0.03. what does the value of 0.42 represent? the population parameter the study is attempting to estimate the margin of error for the survey result the variability of the sampling distribution the total width of the confidence interval the sample statistic obtained from surveyed residents

Explanation:

A confidence interval is constructed as \(\text{Sample Statistic}\pm\text{Margin of Error}\). Here, the confidence interval is given as \(0.42\pm0.03\). The sample statistic (in the case of a proportion confidence interval, it is the sample proportion \(\hat{p}\)) is the center of the confidence interval. The population parameter (the True proportion \(p\) of all Columbus residents who support the plan) is unknown and is what the confidence interval is trying to estimate. The margin of error is \(0.03\) (the value we add and subtract from the sample statistic). The variability of the sampling distribution is related to the standard deviation of the sampling distribution (for a proportion, \(\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\)) and is used in calculating the margin of error. The total width of the confidence interval is \(2\times\text{Margin of Error}=2\times0.03 = 0.06\).

Answer:

The sample statistic obtained from surveyed residents.