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Chapter 1: Problem 8

Determine whether the underlined value is a parameter or a statistic. The average score for a class of 28 students taking a calculus midterm exam was \(72 \%\).

Short Answer

Expert verified
The underlined value (72%) is a parameter because it describes an entire population (the class of 28 students).

Step by step solution

01

Understand the Context

Determine whether the value given (72%) pertains to a sample or an entire population. A parameter describes an entire population, while a statistic describes a sample.
02

Identify the Group

Notice that the problem states the average score for a class of 28 students. Since it mentions the entire class, it implies the entire group concerned with the measurement.
03

Determine the Value Type

Given that the average score is for all 28 students in the class, this measurement describes the entire population of that class. Hence, it is a parameter.

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Key Concepts

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

Population
In statistics, a population refers to the entire group of individuals or items that you are interested in studying. It can be as large as all the people in a country or as small as all the students in a particular classroom.
In the context of our exercise, the population is the entire class of 28 students taking the calculus midterm exam. This means the average score of 72% pertains to all members of this group.
When we talk about a population, we often use the term 'parameter' to describe a characteristic or measure that summarizes the entire group. In our example, since we are considering the whole class, the average score is a parameter.
Sample
A sample is a smaller group selected from the population. It is used when it's impractical or impossible to study the entire population. For example, if we wanted to study student performance in calculus across an entire university, we might select a sample of students from different classes rather than surveying every single student.
In our exercise, if we had only considered the average score of a few students, then that measure would be termed a statistic.
This distinction is crucial for statistical analysis since a sample may not represent the full diversity of the population, leading to potential biases in the conclusions drawn.
Average Score
The average score, also known as the mean, is a measure that summarizes a set of values. It is calculated by adding up all the values and then dividing by the number of values.
In our exercise, the average score of 72% was obtained by adding up all the scores of the 28 students and dividing by 28. This gives us a single number that summarizes the group's performance.
The average score is a useful measure because it provides a central value around which the individual scores are distributed, giving us a quick glimpse of the overall performance of the group.

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Most popular questions from this chapter

Researchers wanted to determine the association between number of times one chews food and food consumption. They identified 45 individuals who were 18 to 45 years of age. First, the researchers determined a baseline for number of chews before swallowing food. Next, each participant attended three sessions to eat pizza for lunch until comfortably full by chewing each portion of food \(100 \%, 150 \%,\) and \(200 \%\) of their baseline number of chews before swallowing. Food intake for each of the three chewing treatments was then measured. It was found that food consumption was reduced significantly, by \(9.5 \%\) and \(14.8 \%,\) respectively, for the \(150 \%\) and \(200 \%\) number of chews compared to the baseline. (a) What is the research objective of the study? (b) What is the response variable in this study? Is it quantitative or qualitative? (c) What is the explanatory variable in this study? Is it quantitative or qualitative? (d) Who are the experimental units? (e) How is control used in this study? (f) Each individual chewed \(100 \%, 150 \%,\) and \(200 \%\) of their baseline number of chews before swallowing. This is referred to as a repeated-measures study since the same participants were exposed to each treatment. The order in which chewing took place ( \(100 \%\) versus \(150 \%\) versus \(200 \%\) ) was determined randomly. Explain why this is important.

To help assess student learning in her developmental math courses, a mathematics professor at a community college implemented pre- and posttests for her students. A knowledge-gained score was obtained by taking the difference of the two test scores. (a) What type of experimental design is this? (b) What is the response variable in this experiment? (c) What is the treatment?

Determine the level of measurement of each variable. Year of birth of college students

It is extremely important for a researcher to clearly define the variables in a study because this helps to determine the type of analysis that can be performed on the data. For example, if a researcher wanted to describe baseball players based on jersey number, what level of measurement would the variable jersey number be? Now suppose the researcher felt that certain players who were of lower caliber received higher numbers. Does the level of measurement of the variable change? If so, how?

Is a television (TV) in the bedroom associated with obesity? Researchers questioned 379 twelve-year old adolescents and concluded that the body mass index (BMI) of the adolescents who had a TV in their bedroom was significantly higher than the BMI of those who did not have a TV in their bedroom. Source: Christelle Delmas, Carine Platat, Brigette Schweitzer, Aline Wagner, Mohamed Oujaa, and Chantal Simon. "Association Between Television in Bedroom and Adiposity Throughout Adolescence," Obesity, \(15: 2495-2503,2007\) (a) Why is this an observational study? What type of observational study is this? (b) What is the response variable in the study? What is the explanatory variable? (c) Can you think of any lurking variables that may affect the results of the study? (d) In the report, the researchers stated, "These results remain significant after adjustment for socioeconomic status." What does this mean? (e) Can we conclude that a television in the bedroom causes a higher body mass index? Explain.
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