Parameters Statistics Biased Unbiased

The characteristic used to describe a sample

• parameter

• statistic

What type of survey sample is it when one portion of the population is favored over another?

• Unbiased sample

• Biased sample

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

• Biased

• Unbiased

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.

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.

The principal at a local high school asked 100 randomly selected students how many minutes they spend completing homework each night of the week. The mean time students in the sample spent on homework each night was 72.5 minutes. Assume the population mean time spent on homework each night is 81.2 minutes. Which of the following is the correct representation of the mean time spent on homework for the 100 randomly selected students in the sample and the population of students at the school?

• 72.5 is a parameter and 81.2 is a statistic

• 72.5 and 100 are both statistics

• 81.2 and 100 and both parameters

• 72.5 is a statistic and 81.2 is a parameter

If a statistic used to estimate a parameter is such that the mean of its sampling distribution is EQUAL to the true value of the parameter being estimated, what is the statistic said to be?

• biased

• unbiased

• random

• proportional

Mrs. Chauvet shows her class a box filled with black and white beads. When she filled the box, 60% of the box consisted of black beads and the rest were white beads. She selected an SRS of 30 beads, and 21 of the 30, or 70%, were black. Which of the following is the correct representation of the percentage of black beads in the box as well the percentage of black beads in her sample?

• 0.6 is a statistic and 0.7 is a parameter

• 0.6 is a parameter and 0.7 is a statistic

• both are parameters

• both are statistics

Biased or Random?

Chloe and Danna want to determine the favorite subject of all students in the middle school. So they place every middle school student's name in a bucket and choose 30 to poll.

• Biased sample

• Random sample

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

• biased

• unbiased