School Improvement in Maryland

Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.

Goal 3 Data Analysis And Probability

Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

Indicator 3.2.1 The student will make informed decisions and predictions based upon the results of simulations and data from research.

Lesson Content

Making Informed Decisions & Predictions Based on Survey Results

Objective

  • Students will make predictions based upon survey results.

Materials Needed

Lesson Structure

    Warm-Up/Opening Activity

    The drill provides a review of sample proportions and making predictions.
    You live in a district with 37,500 voters. Suppose you select a random sample of 1500 voters and find that 900 prefer the democratic candidate running in an upcoming election.
    1. What is the sample proportion?
      (sample proportion: 900/1500=.60)
    2. Estimate the number of voters in your district preferring the democratic candidate using your sample results.
      (estimate of population: 37,500(.60)=22,500)

    Exploration

    When analyzing sample results and estimating population percentages, we are, in fact, making predictions from data. The following activities will enable students to relate rules of probability to estimating from sample results. These exercises provide students with data from random samples from which they can apply rules of probability to make predictions about a population.

    Class Discussion

    It is important to note that in statistics we generally take one sample and make predictions based on these results. Because we take a single sample, it is vital that the procedures used to gather the data rely on simple random sampling techniques. In the real world, there is no way to verify that sample results are good estimates of the true population percentage. If we knew the true percentage in the first place, there would be no reason to sample.

    Formative Assessment

    These questions summarize concepts from several activities and will help the teacher determine if students are grasping the idea of statistical inference.
    Andrew wants to know the number of hours students spend studying outside of school during the week. He asks thirty students in his calculus class to complete a survey. The results are shown below.
     
    # Hours studying in a week 0 - 56 - 1011 - 1516 and over
    # Students41295

     
    1. Identify the population this sample is intended to describe.
      (The population is all students in Andrew's school.)
    2. What is the sample?
      (The sample contains thirty students in Andrew's calculus class.)
    3. According to the survey, what proportion of students study between 6 and 10 hours outside of school in a week?
      (12/30=0.40 or about 40% of students)
    4. There are 1500 students in Andrew's school. Use the survey results to estimate the number of students in the school who study for less than 5 hours per week.
      (According to the sample, about 200 students study for less than 5 hours a week.)
    5. Do you think that Andrew's sample results are good estimates for the population you identified in #1? Use principles of simple random sampling to justify your answer.
      (No. Although Andrew's sample is probably large enough, he selects only calculus students. The sample is biased because calculus students may have study habits that differ significantly from those of other students.)

    Additional Practice

    "Practice Predicting from Survey Results" is an activity that can be used as individual or additional practice if needed.

/share/clg/xml/lesson_plans/mathematics/SurveyResults_321.xml