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  1. Home
  2. 12th grade
  3. Statistics & Probabilities
  4. Exercise : Determine whether samples are biased or unbiased

Determine whether samples are biased or unbiased Statistics & Probabilities

A journalist wants to make a survey to determine the candidate who is the most likely to win the upcoming election. He decides to make a telephone survey and calls every working day at 3 pm.

Is the sample of this survey biased?

When you call at 3 pm, it is more likely to get answers from people who are not working in an office (house-wives, house-husbands, unemployed or retired people). Therefore, the sample is not representative of the whole population.

The sample of this survey is biased.

In a volleyball game, we asked the fans of both teams the following question:

What is your favorite sport? Is this sample biased?

We are asking people who are fans of some volleyball teams. So it is likely to choose volleyball as their favorite sport. So the sample is biased.

The sample of this survey is biased.

In a high school with 1000 students and 25 classes, we randomly choose two students from each class to determine the percentage of students who are planning to attend college after graduation.

Is the sample of this survey biased?

Since we choose the student randomly, these students represent the whole students. So the sample is unbiased.

The sample of this survey is unbiased.

We want to determine the favorite vacation destination of people living in our town. We randomly call 100 people and ask them the question.

Is the sample of the survey biased?

Since we have chosen the people randomly, the sample represent the whole population of the town. So the sample is unbiased.

The sample of this survey is unbiased.

In a small town, 60 percent of the population have access to internet. We make 200 random internet calls to determine if people agree to cut half of the budget for public transportation and devote it to internet infrastructure so that more people in the town connect to the internet.

Is the sample of this survey biased?

We are making an internet call so the sample represent only 60 percent of the population who are likely to choose not to spend more money on internet infrastructure since they already have access to internet.

The sample of this survey is biased.

We want to make a survey and ask people the following question:

What means of transportation do you prefer?

We go to an airport and randomly choose people who are waiting for their flight. Is this sample biased?

Since we choose people from the airport, it is likely that they prefer planes to other means of transportation. So the sample is biased.

The sample of this survey is biased.

We have an amount of money and want to ask university students where to invest this money: athletic programs or music programs? We go to the university restaurant on lunch time and randomly choose one student from each table to make sample.

Is this sample biased?

We randomly choose student from lunch tables. All the students will go to the restaurant for lunch, regardless of their opinion on the topic of the survey. Hence the sample represents all students.

The sample of this survey is unbiased.

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See also
  • Course : Hypothesis testing and estimation
  • Exercise : Use the central limit theorem to find the probability that the sample mean is between two given real numbers
  • Exercise : Find confidence intervals for population means and/or population proportion when the sample size, the standard deviation and the sample mean are given
  • Exercise : Determine the sample size needed for a level of confidence
  • Exercise : Identify whether an experiment is well constructed
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