Optional Task to replace Unit 4 Test

Survey Characteristics

A factory has 3,800 workers. The company needs to change the benefits package. They can offer three plans: A, B and C. They decided to conduct a survey to see which plan the workers like best. They randomly chose 1,000 of the factory workers and asked them this question, “Which benefit plan do you prefer: A, B or C?” They find that 700 prefer plan A, 250 prefer plan B and 50 prefer plan C.

  1. Did they survey the population or a sample?
  2. How many people are in the population of factory workers?
  3. If they surveyed a sample, how many workers are in the sample?
  4. What is the survey question that was asked?
  5. What type of data is collected (parameter or statistic)?
  6. What are the advantages and disadvantages to surveying a sample in this situation?

At a family reunion in Lula, the Carillos count 298 adults and children. They need to have the family reunion somewhere else next year. They narrow down the choices to Gillsville, Gainesville and Clermont. To find out which place the family members prefer, they ask all 298 people at the reunion, “Where would you like the reunion to be held next year: Gillsville, Gainesville or Clermont?” They find that 289 of the 298 people surveyed prefer Gainesville.

  1. Did they survey the population or the sample?
  2. How many people are in the population?
  3. If they surveyed a sample, how many people are in the sample?
  4. They report that about 97% of those surveyed like Gainesville. This is an example of ______. A. Sample C. parameter
  1. Statistic D. Population
  1. What are the advantages and disadvantages to surveying the population in this situation?

After examining eight cartons of eggs at a local supermarket, Sheila concludes that one out of every 12 eggs packaged in the U.S. is cracked.

  1. Did Sheila test the population or the sample?
  2. How many egg cartons are in the population?
  3. If Sheila tested a sample, how many egg cartons are in the sample?
  1. What are the advantages and disadvantages to testing a sample in this situation?

Sample Types

Determine the sample type for each situation. Is the conclusion valid?

  1. To evaluate the quality of their product, a manufacturer of cell phones checks every 50th phone off the assembly line. Out of 200 phones tested, 4 are defective. The manager concludes that about 2% of the cell phones produced will be defective.
  1. To determine whether the students will attend an arts festival at the school, Oliver surveys his friends in the art club. All of Oliver’s friends plan to attend. So, Oliver assumes that all the students at his school will also attend.
  1. To determine what people in California think about a proposed law, 5,000 people from the state are randomly surveyed. Of the people surveyed, 58% are against the law. The legislature concludes that the law should not be passed.
  1. A magazine asks its readers to complete and return a questionnaire about popular television actors. The majority of those who replied liked one actor the most, so the magazine decides to write more articles about that actor.
  1. Marcus wants to predict the next student council president. He polls every fourth person from each grade level as they exit the cafeteria. In his poll, 65% chose Sophia. So, Marcus predicts Sophia will win the election.

Each of the following surveys results in a biased sample. For each situation, explain why the survey is biased. Then explain how you would change the survey to obtain an unbiased sample.

  1. People attending a baseball game were asked if they support the construction of a new stadium in the city.
  1. A record store manager asks customers who make a purchase how many hours of music they listen to each day.
  1. The owner of a company wants to give his workers a paid day off. He suspects that most would prefer to have the day after the Super Bowl off. But he wants to survey the workers to find out which of the following days the most workers would like off: the day after the Super Bowl, February 14 or April 1.

When the owner conducts his survey, which of the following is the least biased question to ask? Why is it the most unbiased? Why are the other three biased?

  1. Would you like a paid day off?
  2. Wouldn’t you like a paid day off on the day after the Super Bowl?
  3. If you are going to get a paid day off, would you like it to be on the day after the Super Bowl or on some other day?
  4. If you are going to get a paid day off, would you like it to be on the day after the Super Bowl, on February 14 or on April 1?

Mean Absolute Deviation Task

For the School Board report, the principal asks every math teacher at Allentown Middle School to estimate the amount of time their students spend studying each week. Allentown’s math teacher, Mrs. Smith, decides to take two samples of 10 students in her math class.

For each sample below:

  1. Make a line plot of the data.
  2. Calculate the Mean.
  3. Calculate the Mean Absolute Deviation.

Sample 1:

Student / About how much time do you spend studying each week? / Absolute Deviation
Sue / 25 minutes
Jorge / 50 minutes
Alex / 50 minutes
Maria / 75 minutes
Tamika / 100 minutes
Sarah / 100 minutes
Beth / 125 minutes
Sam / 125 minutes
Kelly / 150 minutes
Mary / 200 minutes

Mean = ______MAD = ______

Sample 2:

Student / About how much time do you spend studying each week? / Absolute Deviation
Eric / 50 minutes
Marcus / 75 minutes
Carla / 100 minutes
Ben / 125 minutes
Will / 100 minutes
Yasmin / 100 minutes
Jon / 125 minutes
Kayla / 100 minutes
Sara / 100 minutes
Marcus / 75 minutes

Mean = ______MAD = ______

  1. On the back of this page, compare and contrast sample 1 and sample 2. (Be sure to mention the

situation in your explanation.)