Bias vs Unbiased in Math

A company makes DVDs and randomly selects 25 from 1500 to test them to see if they work.

• Biased

• Unbiased

To see who has a computer at home the front office chooses 10 students randomly per grade to ask

• Biased

• Unbiased

To get valid results, a sample must be...

• biased

• unbiased

Convenience sample and voluntary response sample are types of...

• biased samples

• unbiased samples

In a certain school, students can choose whether to eat in the school’s cafeteria. A reporter working for the school’s newspaper polled students on their reactions to changes in the menu at the cafeteria. For each student leaving the cafeteria in one 20-minute time period, the reporter used a die to determine whether to stop the student and ask how he or she felt about the new menu. In the reporter’s article it was stated that a random sample of the students showed that 23% of the school’s student population was happy with the new menu. Which of the following statements is true?

• Because each student leaving the cafeteria was randomly selected and could choose to answer or not, this is a random sample of the student population, and the 23% is an accurate measurement of the school population’s view of the new menu.

• Because students self-selected whether to eat in the cafeteria, the sampling method might be biased and the sample might not be representative of all students in the school.

• The survey would have been more effective if the reporter had collected the data in one 10-minute time period rather than in one 20-minute time period.

• The survey would have been more effective if students who cared about the food could have called the reporter to tell how they felt about the new menu, so that only students with opinions on the subject would have been surveyed.

• Because no treatment was imposed on the students eating in the cafeteria, one cannot make any conclusions about the new menu.

Tanya wants to know the percent of people likely to attend the upcoming musical at school. She asks each person in the musical how many people they know who are coming to make a prediction. Why is this sample biased?

• Drama students are more likely to lie.

• Musicals are better attended than plays.

• The drama teacher was not asked.

• The sample is not random and not representative of the entire school population.

Answer explanation

The sample is not random and not representative of the entire school population, as it only includes people involved in the musical, leading to bias.

Casey surveyed the members of his soccer team to ask them what their favorite sport is. Is this a biased sample or unbiased sample?

• Biased Sample

• Unbiased Sample

To determine how many students at Shull would attend the dance, the principal surveyed the students in Ms. Miller's math class. 10 students said they would attend and 15 said they would not attend. It can be concluded that half the students at Shull will attend the dance. Is this conclusion valid? Why or why not?

• Yes, this is a simple random sample. So the sample is unbiased.

• No, this is a convenience sample. So the sample is unbiased.

• No, this is a voluntary response sample. So the sample is biased.

• No, this is a convenience sample. So the sample is biased.

The Student Council asked every tenth student in the lunch line how they preferred to be contacted with school news. The results are shown in the table. Is this an unbiased sample? If yes, suppose there are 684 students at the school. How many can be expected to prefer E-mail?

• No, it's a biased sample

• 432

• 304

• 16

Ms. Rolf wants to know the average number of siblings her students have, so she assigns each of her students a number 1-72 and uses a random number generator to survey 12 students.

• Biased

• Unbiased