[NW] Government Waste Gallup News Service conducted a survey of 1017 American adolts aged 18 years or older. The respondents were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., do you believe 51 cents or more are wasted?” Of the 1017 individuals surveyed, 35% indicated that 51 cents or more is wasted. Gallup reported that 35% of all adolt Americans 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 4% and a 95% level of confidence.


What is the research objective?

Verified step by step guidance

1. Identify the main purpose of the survey by focusing on what the researchers want to learn from the respondents' answers.
2. Note that the survey asked whether individuals believe that 51 cents or more of every tax dollar is wasted by the federal government.
3. Understand that the research objective is to estimate the proportion of all American adults aged 18 or older who hold this belief about government waste.
4. Recognize that the margin of error and confidence level indicate the precision and reliability of this estimate for the entire population.
5. Summarize the research objective as determining the percentage of American adults who think the federal government wastes at least 51 cents of every tax dollar.

Key Concepts

Research Objective

The research objective defines the main goal or purpose of a study. It specifies what the researcher aims to discover or understand, such as measuring public opinion or estimating a population parameter. In this question, the objective is to assess the proportion of American adults who believe the government wastes a significant portion of tax dollars.

Margin of Error

The margin of error quantifies the range within which the true population parameter is expected to lie, based on the sample data. It reflects sampling variability and indicates the precision of the estimate. Here, a 4% margin of error means the reported 35% could vary by plus or minus 4 percentage points in the population.

Confidence Level

The confidence level represents the degree of certainty that the population parameter lies within the margin of error around the sample estimate. A 95% confidence level means that if the survey were repeated many times, 95% of the intervals calculated would contain the true population proportion. It reflects the reliability of the estimate.