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Chapter 11: Problem 6

Determine whether the sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative. A political scientist wants to know how a random sample of 18- to 25-year-olds feel about Democrats and Republicans in Congress. She obtains a random sample of 1030 registered voters 18 to 25 years of age and asks, 鈥淒o you have favorable/unfavorable [rotated] opinion of the Democratic/Republican [rotated] party?鈥� Each individual was asked to disclose his or her opinion about each party.

Short Answer

Expert verified
Dependent sampling; qualitative response variable.

Step by step solution

01

Identify the sampling method

The political scientist is taking a random sample of 1030 registered voters aged 18 to 25. Each individual in the sample provides opinions about both political parties.
02

Determine if the sampling is dependent or independent

Since each individual in the sample is providing an opinion on both the Democratic and Republican parties, the sampling is dependent. This is because the responses are related; one person's opinions influence both responses (they are not independent observations).
03

Identify the response variable

The response variable is the opinion on the Democratic or Republican party. It is whether the opinion is favorable or unfavorable.
04

Determine if the response variable is qualitative or quantitative

The response variable is qualitative because it categorizes the opinion of the participants as 'favorable' or 'unfavorable', which are non-numerical labels.

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Key Concepts

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

qualitative variable
In this exercise, the political scientist asks individuals whether they have a favorable or unfavorable opinion about the Democratic and Republican parties. These responses are considered qualitative variables.
Qualitative variables are attributes or characteristics that describe the quality of something. They are not numbers but categories or labels.
For example, in this study, 'favorable' and 'unfavorable' are the categories. Because these responses do not have a numerical value, they are qualitative.
Another example of a qualitative variable can be the type of car you drive (SUV, sedan, truck, etc.).
It鈥檚 important to recognize qualitative variables because analyzing them usually involves different methods compared to numerical data.
response variable
The response variable in this survey is the opinion about the political parties. Specifically, it is whether the respondent's opinion is favorable or unfavorable.
A response variable, also known as a dependent variable, is the main variable of interest in an experiment or study. It is the variable the researcher is trying to explain or understand.
In the context of the given exercise, the response variable is the opinion about each political party. It changes based on individuals' perceptions and feelings.
Understanding the response variable is crucial because it directly influences how you analyze the data and draw conclusions from the study.
random sampling
Random sampling plays a significant role in the accuracy of this study. The political scientist obtained a random sample of 1030 registered voters aged 18 to 25.
Random sampling means that each member of the population has an equal chance of being selected in the sample. This method helps to ensure the sample is representative of the larger population.
Using random sampling reduces bias and makes the results more generalizable to a broader group.
For instance, if the political scientist did not use random sampling and chose only participants from a specific university, the results might not represent the views of all 18- to 25-year-olds.

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Most popular questions from this chapter

In March \(2003,\) the Pew Research Group surveyed 1508 adult Americans and asked, "Do you believe the United States made the right or wrong decision to use military force in Iraq?" Of the 1508 adult Americans surveyed, 1086 stated the United States made the right decision. In August \(2010,\) the Pew Research Group asked the same question of 1508 adult Americans and found that 618 believed the United States made the right decision. (a) In the survey question, the choices "right" and "wrong" were randomly rotated. Why? (b) Construct and interpret a \(90 \%\) confidence interval for the difference between the two population proportions, \(p_{2003}-p_{2010^{\circ}}\)

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For each study, explain which statistical procedure (estimating a single proportion; estimating a single mean; hypothesis test for a single proportion; hypothesis test for a single mean; hypothesis test or estimation of two proportions, hypothesis test or estimation of two means, dependent or independent) would most likely be used for the research objective given. Assume all model requirements for conducting the appropriate procedure have been satisfied. What proportion of registered voters is in favor of a tax increase to reduce the federal debt?

Sugary Beverages It has been reported that consumption of sodas and other sugar-sweetened beverages cause excessive weight gain. Researchers conducted a randomized study in which 224 overweight and obese adolescents who regularly consumed sugar-sweetened beverages were randomly assigned to experimental and control groups. The experimental groups received a one-year intervention designed to decrease consumption of sugar-sweetened beverages, with follow-up for an additional year without intervention. The response variable in the study was body mass index (BMI-the weight in kilograms divided by the square of the height in meters). Results of the study appear in the following table. Source: Cara B. Ebbeling, \(\mathrm{PhD}\) and associates, "A Randomized Trial of Sugar-Sweetened Beverages and Adolescent Body Weight" N Engl J Med 2012;367:1407-16. DOI: 10.1056/NEJMoal2Q3388 $$ \begin{array}{lll} & \text { Experimental } & \text { Control } \\ & \text { Group } & \text { Group } \\ & (n=110) & (n=114) \\ \hline \text { Start of Study } & \text { Mean BMI }=30.4 & \text { Mean BMI }=30.1 \\ & \text { Standard Deviation } & \text { Standard Deviation } \\ & \mathrm{BMI}=5.2 & \mathrm{BMI}=4.7 \\ \hline \text { After One Year } & \text { Mean Change in } & \text { Mean Change in } \\ & \mathrm{BMI}=0.06 & \mathrm{BMI}=0.63 \\ & \text { Standard Deviation } & \text { Standard Deviation } \\ & \text { Change in } & \text { Change in } \\ & \mathrm{BMI}=0.20 & \mathrm{BMI}=0.20 \\ \hline \text { After Two Years } & \text { Mean Change in } & \text { Mean Change in } \\ & \mathrm{BMI}=0.71 & \mathrm{BMI}=1.00 \\ & \text { Standard Deviation } & \text { Standard Deviation } \\ & \text { Change in } & \text { Change in } \\ & \mathrm{BMI}=0.28 & \mathrm{BMI}=0.28 \end{array} $$ (a) What type of experimental design is this? (b) What is the response variable? What is the explanatory variable? (c) One aspect of statistical studies is to verify that the subjects in the various treatment groups are similar. Does the sample evidence support the belief that the BMIs of the subjects in the experimental group is not different from the BMIs in the control group at the start of the study? Use an \(\alpha=0.05\) level of significance. (d) One goal of the research was to determine if the change in BMI for the experimental group was less than that for the control group after one year. Conduct the appropriate test to see if the evidence suggests this goal was met. Use an \(\alpha=0.05\) level of significance. What does this result suggest? (e) Does the sample evidence suggest the change in BMI is less for the experimental group than the control group after two years? Use an \(\alpha=0.05\) level of significance. What does this result suggest? (f) To what population do the results of this study apply?

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