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When conducting a survey, care must be taken so that bias is not introduced through choice of sample or through the survey questions. If a survey is used to make inferences, it is necessary to estimate how accurate the results are.

Data in a survey is collected by having participants answer questions. If the questions are written so that they affect the answers, the questions are biased. To avoid this, questions should be written so that

- there is no implication of there being a certain answer that is favorable or correct,
- the person who answers has the necessary knowledge to answer the question, and
- the participants answer truthfully even if the subject is sensitive.

Identify and correct the bias in the following two survey questions.

- Question in a health study. "Research shows that it is beneficiary to your health to exercise regularly. How many times a week do you exercise?"
- Question in a survey about attitudes, conducted by a math teacher in a class he teaches. "Do you like mathematics?"

Show Solution

"Rank the following school subjects by writing the numbers 1 to 4 on the line. 1 indicating your favorite subject and 4 your least favorite.

___ English

___ Mathematics

___ Chemistry

___ History"

When the mean value can be determined for a specific characteristic of a population, this is referred to as a population mean. For example, it is possible to measure the height of all citizens of North Dakota. The population mean would be the average height of all North Dakotans.

A population is often not uniform. Some characteristics include

- age,
- gender,
- income,
- marital status, and/or
- religion.

A survey only targets a sample of the population. Therefore, when using survey data to make inferences, there is always uncertainty in the results. The larger the sample is, the more reliable the results are. Margin of error is an estimate of how much the responses from the sample at most will differ from those of the population. With the sample size n, the margin of error can be approximated by this formula.

$Margin of error=±n 1 $

The director Selma Omm has just finished the production of her latest movie, Galactic War IV. A test screening was held for high school students, the typical audience for the Galactic War movies. When asked what they thought of the character Tom Ent, 72 of 360 students said they liked him. Determine and interpret the margin of error in this survey.

Show Solution

Out of the 360 who watched the screening, 72 liked Tom Ent. We can calculate the percent this represents.
Thus, 20 % of the audience in the screening liked him. The margin of error depends on the population size, n. In this case it is the total audience in the screening, 360.

$Margin of error=±n 1 =±360 1 ≈±0.05$

It can be expected that the character Tom Ent will be liked by somewhere in the interval 0.2−0.05=0.15=15 % and 0.2+0.05=0.25=25 % of the total audience of the movie.
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