Samples and

Surveys

Section 11.8

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Data Sets

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Population

The collection of all responses, measurements, or counts that are of interest.

SampleA portion or subset of the population.

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Example: Identifying Data Sets

In a recent survey, 1500 adults in the United States were asked if they thought there was solid evidence for global warming. Eight hundred fifty-five of the adults said yes. Identify the population and the sample. Describe the data set. (Adapted from: Pew Research Center)

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Solution: Identifying Data SetsThe population consists of the responses of all adults in the U.S.

The sample consists of the responses of the 1500 adults in the U.S. in the survey.

The sample is a subset of the responses of all adults in the U.S.

The data set consists of 855 yes’s and 645 no’s.

Responses of adults in the U.S. (population)

Responses of adults in survey (sample)

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Sampling Types and Methods

Convenience Sampling: select any members of the population who are conveniently and readily available

Self-Selected Sample: select only members of the population who volunteer for the sample

Systematic Sample: order the population in some way, and then select from it at regular intervals

Random Sample: all members of the population are equally likely to be chosen

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Bias

Bias: systematic error introduced by the sampling method

A sample has a bias when a part of a population is overrepresented or underpresented.

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Analyzing Sampling Methods

A newspaper wants to find out what percent of the city population favors a property tax increase to raise money for local parks. What is the sampling method used for each situation? Does the sample have a bias? Explain.

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A newspaper article on the tax increase invites readers to express their opinion s on the newspaper’s website.

Self-selected sample

Bias: depending on who visits the website

Example: Some property owners who are against the tax might organize a campaign to get friends and neighbors to visit the website.

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A reporter interviews people leaving the city’s largest park.

Convenience Sample

Bias: The sample may overrepresent park supporters because it is near a park.

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A survey service calls every 50th listing from the local phone book.

Systematic Sample

Bias: May if there is some link between people who are listed in a phone book and people who pay property taxes.

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Data Collection

Observational study A researcher observes and measures characteristics

of interest of part of a population but does not change existing conditions.

You measure or observe members of a sample in such a way that they are not affected by the study.

Researchers observed and recorded the mouthing behavior on nonfood objects of children up to three years old. (Source: Pediatric Magazine)

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Data Collection

Controlled Experiment

You divide the sample into two groups. A treatment is applied to part of a population and responses are observed.

You impose a treatment on one group but not on the other “control” group. Then you compare the effect on the treated group to the control group.

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Controlled Experiment

An experiment was performed in which diabetics took cinnamon extract daily while a control group took none. After 40 days, the diabetics who had the cinnamon reduced their risk of heart disease while the control group experienced no change. (Source: Diabetes Care)

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Control Group: no treatment is applied; they can be given placebo (harmless, unmedicated treatment that is made to look like the real treatment)

Treatment Group: part of the population in which treatment is applied

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Data Collection

Survey

You ask every member of the sample a set of questions.

Commonly done by interview, mail, or telephone.

A survey is conducted on a sample of female physicians to determine whether the primary reason for their career choice is financial stability.

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Analyzing Study Methods

Which type of study method is described in each situation? Should the sample statistics be used to make a general conclusion about the population?

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Researchers randomly choose two groups from 10 volunteers. Over a period of 8 weeks, one group eats ice cream before going to sleep, and the other does not. Volunteers wear monitoring devices while sleeping, and researchers record dream activity.

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Controlled Experiment

The statistics for this study are based on such a small sample that the findings are unreliable as a general conclusion.

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Students in a science class record the height of bean plants as they grow.

Observational Study

The statistics may provide a general conclusion about the growth rate of a bean plant. However soil type, amount of sunlight and water, fertilizer, and other factors could affect the growth rate.

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Student council members ask every tenth student in the lunch line if they like the cafeteria food.

Survey

The results are not reliable because people waiting in line are more likely to enjoy the cafeteria food than those who brought their lunch from home.

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Designing a Survey

During the 2008 Olympic Games, a U.S. swimmer won more medals than any other swimmer in history. What sampling method could you use to find the percent of students in your school who recognize that swimmer from a photograph? What is an example of a survey question that is likely to yield information that has no bias?

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A possible sampling method is to question every 10th student entering school in the morning. This is a systematic sampling. It usually contains the least bias. A possible unbiased survey question is. “Who is pictured in this photograph?”

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Exit TicketIdentify the sampling method. Then identify any bias in each method.1. A supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting card aisle.

2. A maintenance crew wants to estimate how many of 3000 air filters in a 30-story office building need replacing. The crew examines five filters chosen at random on each floor of the building.

Identify the type of study method described in each situation and explain whether the sample statistics can be used to make a general conclusion about the population.3. A list of students is randomly generated from the school database. Information for every student is entered into the database, and each student has an equally likely chance of being selected. The students selected are asked how much time they spend on household chores each week.

4. The local librarian collects data about the types of books that are checked out so that she can place a new book order accordingly. She records the type of book checked out by every other person each day for three weeks.

5. A gardener tests a new plant food by planting seeds from the same package in the same soil and location. Each plant is given the same amount of water, but one plant is given good and the other is given no food at all. He records the growth and flowering rates of each plant.

6. What sampling method could you use to find the percent of residents in your neighborhood who recognize the governor of your state by name? What is an example of a survey question that is likely to yield information that has no bias?

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