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Gallup News Service conducted a survey of 1017 American adults aged 18 years or older, September \(4-7,2014 .\) The respondents were asked, "Of every tax dollar that goes to the federal government in Washington, D.C. how many cents of each dollar would you say are wasted?" Of the 1017 individuals surveyed, \(35 \%\) indicated that 51 cents or more is wasted. Gallup reported that \(35 \%\) of all adult 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. (a) What is the research objective? (b) What is the population? (c) What is the sample? (d) List the descriptive statistics. (e) What can be inferred from this survey?

Step by step solution

01

Determine the Research Objective

The research objective refers to the goal or purpose of the survey. It is the main question that the researchers aim to answer through their study. In this case, the objective is to find out what percentage of American adults believe that the federal government wastes at least 51 cents of every tax dollar.

02

Identify the Population

The population consists of all possible subjects that the researchers want to study. Here, the population is all American adults aged 18 years or older.

03

Identify the Sample

The sample is a smaller group selected from the population, which is used to gather data and make inferences about the entire population. The sample in this case is 1017 American adults aged 18 years or older who were surveyed from September 4-7, 2014.

04

List the Descriptive Statistics

Descriptive statistics are numbers that summarize the data collected through the survey. For this survey, the key descriptive statistic is that 35% of the surveyed individuals believe that 51 cents or more of each tax dollar is wasted.

05

Make Inferences from the Survey

Inference involves making conclusions about the population based on the sample data. From this survey, it can be inferred with 95% confidence that between 31% and 39% (35% ± 4%) of all American adults believe that the federal government wastes at least 51 cents of each dollar spent.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Research Objective

The research objective is essentially the big question the survey aims to answer. In this case, the goal of the Gallup survey was to determine how many American adults think that the federal government wastes at least 51 cents of every tax dollar. This objective helps guide the survey design and focuses the analysis on specific data points. By knowing the objective, you can better understand what the survey is trying to reveal about public opinion on government spending and waste.

Population

The population in a research study includes all the subjects that the researchers are interested in. Here, the population consists of all American adults aged 18 years or older. This is a broad group that includes millions of individuals. The population defines the scope of the study and ensures that the results can be generalized to everyone in that category. Identifying the population correctly is essential to conducting a meaningful survey and obtaining relevant results.

Sample

A sample is a smaller, manageable group drawn from the larger population that researchers study to make predictions or inferences about the population as a whole. In the Gallup survey, the sample is made up of 1017 American adults aged 18 or older, surveyed between September 4-7, 2014. Choosing a representative sample is crucial to the reliability of the survey results. A good sample accurately reflects the diversity and characteristics of the entire population, which allows researchers to generalize their findings with confidence.

Inference

Inference involves drawing conclusions about a population based on the data from a sample. From this survey, researchers can infer that between 31% and 39% (taking into account the 4% margin of error) of American adults believe the federal government wastes at least 51 cents of every tax dollar. This inference is made with a 95% level of confidence, which means that if the survey were repeated numerous times, 95% of the results would fall within this range. Inference helps translate sample findings into meaningful insights about the broader population.