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Chapter 1: Problem 41

A research objective is presented. For each, identify the population and sample in the study. A farmer interested in the weight of his soybean crop randomly samples 100 plants and weighs the soybeans on each plant.

Short Answer

Expert verified
The population is all the plants in the farmer's crop, and the sample is the 100 soybean plants he randomly sampled.

Step by step solution

01

Identify the Population

The population is the entire group that the farmer is interested in studying. In this case, the farmer is interested in the weight of the soybeans on all the plants in his entire crop.
02

Determine the Sample

The sample is the subset of the population that the farmer actually examines. Here, the farmer randomly samples 100 soybean plants from his crop and weighs the soybeans on each of these plants.

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Key Concepts

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

Population
In statistics, the term 'population' refers to the entire group that you want to draw conclusions about. For example, if you are studying the average weight of soybeans in a farmer's crop, then all the soybean plants in the crop represent the population.
Think of a population as the big picture.
It includes every unit or individual that fits the criteria of your study. For the farmer, it means every single soybean plant growing on his land.
  • Population in our example: All soybean plants in the farmer's entire crop.
Understanding the population is vital because it sets the scope of your research.
It helps you understand the breadth of data from which you could potentially draw insights.
Sample
A 'sample' is a portion or subset of the population that you actually examine or measure. In our example, the farmer doesn't weigh all soybean plants. Instead, he selects a smaller group鈥�100 plants鈥攁nd measures the weight of soybeans from this group.
Working with a sample can save a lot of time and resources.
It's often impractical or impossible to collect data from an entire population. By using a sample, you can still gather meaningful insights while managing work efficiently.
  • Sample in our example: 100 randomly selected soybean plants.
A good sample should represent the population well.
This means the sample should have similar characteristics to the entire population, so conclusions drawn from the sample can be generalized back to the whole group.
Random Sampling
Random Sampling is a method of selecting a sample in such a way that every member of the population has an equal chance of being chosen.
It helps prevent bias, making the sample more representative of the population.
In our example, when the farmer randomly selects 100 soybean plants, he ensures that each plant has an equal opportunity to be included in the sample.
  • Why use random sampling? It reduces bias and increases the likelihood that the sample accurately reflects the population.
Random sampling is a cornerstone of statistical analysis.
Without it, results could be skewed by systematic errors or biases, making them unreliable.
By ensuring randomness, you get a clearer, more accurate picture that can be generalized to the entire population.

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Most popular questions from this chapter

In Problems 11-22, identify the type of sampling used.To predict the outcome of a county election, a newspaper obtains a list of all 945,035 registered voters in the county and wants to conduct a systematic sample. (a) Determine \(k\) if the sample size is 130 . (b) Determine the individuals who will be administered the survey. More than one answer is possible.

In Problems 11-22, identify the type of sampling used. The presider of a guest-lecture series at a university stands outside the auditorium before a lecture begins and hands every fifth person who arrives, beginning with the third, a speaker evaluation survey to be completed and returned at the end of the program.

Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. The following information relates to the 2011 model year product line of BMW automobiles.$$\begin{array}{llcc}\text { Model } & \text { Body Style } & \text { Weight (lb) } & \text { Number of Seats } \\\\\hline \text { 3 Series } & \text { Coupe } & 3362 & 4 \\\\\hline \text { 5 Series } & \text { Sedan } & 4056 & 5 \\\\\hline \text { 6 Series } & \text { Convertible } & 4277 & 4 \\\\\hline \text { 7 Series } & \text { Sedan } & 4564 & 5 \\\\\hline \text { X3 } & \text { Sport utility } & 4012 & 5 \\\\\hline \text { Z4 } & \text { Roadster } & 3505 & 2 \\\& \text { Coune } &\end{array}$$

The following abstract appears in The New England Journal of Medicine: BACKGROUND. The relation between passive smoking and lung cancer is of great public health importance. Some previous studies have suggested that exposure to environmental tobacco smoke in the household can cause lung cancer, but others have found no effect. Smoking by the spouse has been the most commonly used measure of this exposure. METHODS. In order to determine whether lung cancer is associated with exposure to tobacco smoke within the household, we conducted a case-control study of 191 patients with lung cancer who had never smoked and an equal number of persons without lung cancer who had never smoked. Lifetime residential histories including information on exposure to environmental tobacco smoke were compiled and analyzed. Exposure was measured in terms of "smokeryears," determined by multiplying the number of years in each residence by the number of smokers in the household. RESULTS. Household exposure to 25 or more smoker-years during childhood and adolescence doubled the risk of lung cancer. Approximately 15 percent of the control subjects who had never smoked reported this level of exposure. Household exposure of less than 25 smoker-years during childhood and adolescence did not increase the risk of lung cancer. Exposure to a spouse's smoking, which constituted less than one third of total household exposure on average, was not associated with an increase in risk. CONCLUSIONS. The possibility of recall bias and other methodologic problems may influence the results of casecontrol studies of environmental tobacco smoke. Nonetheless, our findings regarding exposure during early life suggest that approximately 17 percent of lung cancers among nonsmokers can be attributed to high levels of exposure to cigarette smoke during childhood and adolescence. (a) What is the research objective? (b) What makes this study a case-control study? Why is this a retrospective study? (c) What is the response variable in the study? Is it qualitative or quantitative? (d) What is the explanatory variable in the study? Is it qualitative or quantitative? (e) Can you identify any lurking variables that may have affected this study? (f) What is the conclusion of the study? Can we conclude that exposure to smoke in the household causes lung cancer? (g) Would it be possible to design an experiment to answer the research question in part (a)? Explain.

Consider the following two questions: (a) Do you believe that the government should or should not be allowed to prohibit individuals from expressing their religious beliefs at their place of employment? (b) Do you believe that the government should or should not be allowed to prohibit teachers from expressing their religious beliefs in public school classrooms? Do you think the order in which the questions are asked will affect the survey results? If so, what can the pollster do to alleviate this response bias? Discuss the choice of the word prohibit in the survey questions.
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