Question

The goal of statistics is to use data to understand something about the world. To obtain...

The goal of statistics is to use data to understand something about the world. To obtain useful results, a scientific approach should be followed. The basic approach can be summarized into a few steps.

  1. Write a question that can be answered by collecting data.
  2. Determine what variables to measure and how to collect a data sample.
  3. Analyze the data and create appropriate summaries.
  4. Create a report of the results, drawing conclusions or inferences where appropriate.

For example, suppose you are the owner of a small business that helps local farmers sell their produce at grocery stores in a city. The farmers are interested in knowing what crops they should produce and look to you to help provide some guidance. This type of question can be better understood using statistical analysis. The four steps of the statistical process are described in general and then applied to this situation in the table below.

Write a question

Writing a question or claim involves identifying the group of items or individuals of interest, or the population. Then, you must determine what kind of information about that population is important. The group of interest is the people living in the city who shop for food at grocery stores. To help the farmers, you need to answer the question "What kinds of produce do those people buy and in what amounts?"
Determine what variables to measure and how to collect the data

Variables are properties or attributes of the individuals in the population that can be measured. To obtain data, a sample of the population must be chosen and the variables that are important to the situation should be recorded for each individual in the sample.

It is important that the sample be representative of the population and that it not be subject to bias. Bias is introduced when some part of the population is over or under represented.

To answer the question, the variables should include the amounts of each kind of produce being purchased.

An appropriate sampling method would be to go to each of the grocery stores in the city and survey a random sample of the people making purchases at the store.

Since the growing season is limited to a particular time of year, the survey should be conducted during a time when the crops would be available from the farmers.

Analyze the data
Analysis of the data involves calculating appropriate summaries for the variables. For numeric variables this includes calculating averages and typical ranges for the variable. For other variables, the summaries may involve charts of the distribution of the values. Since the quantity of produce purchased is a numeric variable, it would be appropriate to create summaries of the average amounts and their ranges. It would also be helpful to the farmers to see the relative percentages of each kind of produce, so charts showing the distribution of different kinds of produce should be created.
Draw conclusions
When a sample is randomly selected without bias, then it should be representative of the population. For reasonably large sample sizes, the results should be generalizable to the population. The sampling method here used randomly selected shoppers at the stores in the city, so the result should be representative of the population. The results should be generalizable to all shoppers.

Evaluate the sampling method

Question

When collecting the data, you choose a Saturday morning and send a person to each of the five stores in the city. You have them use a die to choose the people to interview by rolling the die each time a person leaves the store and only interviewing a person if the roll is a 1. Will this method produce a random sample that is representative of the population?

Solution

While the die-rolling method is a reasonable way to randomly choose shoppers leaving the store, there is a problem with the sampling method. The shoppers in the sample will all be from people who were shopping on Saturday morning. The sampling method could result in a biased sample.

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Identify and describe the steps in the statistical analysis process

Question

A statistics student is doing a project for her class. She wants to make a prediction for the outcome of an upcoming national election. Since there are only two candidates, she decides that her question is "Which candidate do more people favor in the upcoming election?" She decides to randomly interview 100 students crossing the courtyard on campus about their preference. Is this sample good for drawing general conclusions about the results of the election?

Select the correct answer below:

Yes. Since the people in the sample are chosen randomly, the sample should represent the population.

No. The results are not generalizable because the students at her school are not representative of the population of all voters.

No. The results are not generalizable because too few people are interviewed.

No. The results are not generalizable because too many people are interviewed.

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Homework Answers

Answer #1

The answer

No. The results are not generalizable because the students at her school are not representative of the population of all voters.

Explanation

1. The Question set by her can be considered relevant

2. How to collect the data: This point was not properly followed. Instead of random sampling she has used convenient sampling, which is biased and cannot be statistically analysed properly. Also the sample is not a representative sample of the population

3. Since step number 2 is wrong the next two steps of analysig and conclusion will also become biassed and will lead to wrong analysis

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