Statistics 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

To determine the number of umbrellas the average household in the United States owns, a survey of 100 randomly selected households in Arizona is conducted. Of the households, 24 said that they own 3 or more umbrellas. The researcher concluded that 24% of the households in the United States own 3 or more umbrellas. Is the this a valid conclusion? Justify your answer.

• Valid. The sample is biased.

• Not valid. The sample is biased.

• Valid. The sample is unbiased.

• Not valid. The sample is unbiased.

Is this sample biased or unbiased?

A sample of 50 students who currently have an A in math.

• Biased

• Unbiased

Is this sample biased or unbiased?

A sample of 50 randomly selected students.

• Biased

• Unbiased

What is: A group from a population that does not accurately represent the entire population.

• biased sample

• compound event

• population

• dependent

Which of these statements best describes a biased sample?

• It is very small.

• It is not randomly chosen.

• It results in incorrect predictions.

• It does not accurately represent the population.

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.

At a middle school, the administration wants to know how most students get to school. Which sample would be considered a biased sample?

• every 10th student entering the library

• every 10th student getting off a bus

• every fifth student from an alphabetical list

• one student randomly chosen from every homeroom

Ms. Madson wants to know how many students will attend the next 7^th grade after school dance.  She places all the 7^th grade students’ names in a jar and selects 50. Is this random or biased sampling?

• Random

• Biased

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.