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Chapter 1: Problem 18

Suppose you want to estimate the percentage of videos on YouTube that are cat videos. It is impossible for you to watch all videos on YouTube so you use a random video picker to select 1000 videos for you. You find that \(2 \%\) of these videos are cat videos.Determine which of the following is an observation, a variable, a sample statistic (value calculated based on the observed sample), or a population parameter. (a) Percentage of all videos on YouTube that are cat videos. (b) \(2 \%\). (c) A video in your sample. (d) Whether or not a video is a cat video.

Short Answer

Expert verified
(a) Population parameter, (b) Sample statistic, (c) Observation, (d) Variable.

Step by step solution

01

Identify Population Parameter

The population parameter is a characteristic of the entire population, which includes all the videos on YouTube. In this context, it refers to the overall percentage of videos on YouTube that are cat videos. Since we are interested in the actual percentage and cannot determine it exactly from a sample, this is the population parameter. Thus, the answer is part (a): The percentage of all videos on YouTube that are cat videos.
02

Identify Sample Statistic

A sample statistic is a value that describes a characteristic of a sample, which in this case is the 1000 randomly selected videos. Since we found that 2% of these videos are cat videos, this is our sample statistic. Therefore, part (b): \(2\%\) is the sample statistic.
03

Identify Observation

An observation is a single data point collected from the sample. Here, each individual video is a single observation. Thus, part (c): A video in your sample is an observation.
04

Identify Variable

A variable is a characteristic that can vary, it can be qualitative or quantitative. In this context, whether a video is a cat video or not can change from video to video. Hence, part (d): Whether or not a video is a cat video is the variable.

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Key Concepts

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

Population Parameter
When we discuss a population parameter, we refer to a value that provides information about an entire group or collection. In statistical inference, the population parameter is often what researchers or statisticians aim to estimate or learn about. In our exercise scenario, this could include every single video on YouTube. This is a daunting task, which is why we sample a smaller portion of videos to make educated guesses about the population.
  • The population parameter is hypothetical because it can't be known unless every element of the population is measured, which is usually impractical.
  • It serves as a target of inference. We use samples to draw conclusions about this overarching characteristic.
In this case, the percentage of all videos on YouTube that are cat videos represents the population parameter.
Sample Statistic
A sample statistic is a numerical value that summarizes a particular feature of the sample. Samples are selected randomly to represent the population, making inferences about the larger group more feasible and less costly.
  • The sample statistic provides an estimate of the population parameter, although it is not exact.
  • By analyzing the statistic, like our 2% cat video finding in the exercise scenario, we can infer possible characteristics of the entire population.
In this instance, when we identify that 2% of the 1000 sampled videos are cat videos, this percentage is deemed our sample statistic. This number serves as an approximation of what might be the case across all YouTube videos.
Observation
An observation refers to a single data point within a given sample. Observations are fundamental units of data collection and analysis. They help us form a more detailed and individual understanding of the sample composition.
  • Each observation contributes to the overall understanding of the sample as a whole.
  • When aggregated, observations allow us to calculate the sample statistic.
In our exercise, each video randomly selected from YouTube serves as an observation, representing part of our data collection effort to infer about the entire platform's video content.
Variable
In statistics, a variable is a feature or characteristic that can have various values. Variables can be qualitative, describing qualities or categories, or quantitative, indicating quantities and numerical measures.
  • Variables are essential in forming hypotheses and analyzing data.
  • They allow statisticians to categorize and quantify different data points.
Within our example, whether or not a video is a cat video is a variable. It can vary from one observed video to another, highlighting the diverse content that may exist within our sample.

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Most popular questions from this chapter

Identify the flaw(s) in reasoning in the following scenarios. Explain what the individuals in the study should have done differently if they wanted to make such strong conclusions. (a) Students at an elementary school are given a questionnaire that they are asked to return after their parents have completed it. One of the questions asked is, "Do you find that your work schedule makes it difficult for you to spend time with your kids after school?" Of the parents who replied, \(85 \%\) said "no". Based on these results, the school officials conclude that a great majority of the parents have no difficulty spending time with their kids after school. (b) A survey is conducted on a simple random sample of 1,000 women who recently gave birth, asking them about whether or not they smoked during pregnancy. A follow-up survey asking if the children have respiratory problems is conducted 3 years later, however, only 567 of these women are reached at the same address. The researcher reports that these 567 women are representative of all mothers. (c) An orthopedist administers a questionnaire to 30 of his patients who do not have any joint problems and finds that 20 of them regularly go running. He concludes that running decreases the risk of joint problems.

The following summary table shows the number of space launches in the US by the type of launching agency and the outcome of the launch (success or failure). (a) What variables were collected on each launch in order to create to the summary table above? (b) State whether each variable is numerical or categorical. If numerical, state whether it is continuous or discrete. If categorical, state whether it is ordinal or not. (c) Suppose we wanted to study how the success rate of launches vary between launching agencies and over time. In this analysis, which variable would be the response variable and which variable would be the explanatory variable?

A survey was conducted to study the smoking habits of UK residents. Below is a data matrix displaying a portion of the data collected in this survey. Note that " \(拢 "\) stands for British Pounds Sterling, "cig" stands for cigarettes, and "N/A" refers to a missing component of the data. \({ }^{17}\) $$ \begin{array}{rccccccc} \hline & \text { sex } & \text { age } & \text { marital } & \text { grossIncome } & \text { smoke } & \text { amtWeekends } & \text { amtWeekdays } \\ \hline 1 & \text { Female } & 42 & \text { Single } & \text { Under } 拢 2,600 & \text { Yes } & 12 \text { cig/day } & 12 \text { cig/day } \\ 2 & \text { Male } & 44 & \text { Single } & 拢 10,400 \text { to } 拢 15,600 & \text { No } & \text { N/A } & \text { N/A } \\ 3 & \text { Male } & 53 & \text { Married } & \text { Above } 拢 36,400 & \text { Yes } & 6 \text { cig/day } & 6 \text { cig/day } \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ 1691 & \text { Male } & 40 & \text { Single } & 拢 2,600 \text { to } 拢 5,200 & \text { Yes } & 8 \text { cig/day } & 8 \text { cig/day } \\ \hline \end{array} $$ (a) What does each row of the data matrix represent? (b) How many participants were included in the survey? (c) Indicate whether each variable in the study is numerical or categorical. If numerical, identify as continuous or discrete. If categorical, indicate if the variable is ordinal.

A large college class has 160 students. All 160 students attend the lectures together, but the students are divided into 4 groups, each of 40 students, for lab sections administered by different teaching assistants. The professor wants to conduct a survey about how satisfied the students are with the course, and he believes that the lab section a student is in might affect the student's overall satisfaction with the course. (a) What type of study is this? (b) Suggest a sampling strategy for carrying out this study.

Exercise 1.4 introduces a study on using the Buteyko shallow breathing technique to reduce asthma symptoms and improve quality of life. As part of this study 600 asthma patients aged \(18-69\) who relied on medication for asthma treatment were recruited and randomly assigned to two groups: one practiced the Buteyko method and the other did not. Those in the Buteyko group experienced, on average, a significant reduction in asthma symptoms and an improvement in quality of life. (a) Identify the population of interest and the sample in this study. (b) Comment on whether or not the results of the study can be generalized to the population, and if the findings of the study can be used to establish causal relationships.
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