Media Polls Worksheet

  1. A news report states that based on a recent survey of randomly selected high school seniors, it is estimated that 30% of all seniors drink alcohol on a regular basis (margin of error ± 3.5%).

    a) Identify the population and the sample.

    b) Identify the parameter and the statistic.

    c) What reliability (or confidence) do you associate with this result?

    d) Must it be true that between 26.5% and 33.5% of all high school seniors drink alcohol on a regular basis?

    e) A friend asks you what this result means. Explain…without resorting to any symbols or formulas.

  2. A public interest group is interested in people’s opinions about gun control. Random samples of voting age citizens are drawn in each of 3 states: Texas, Montana and New York. Each person is asked "Do you favor tougher gun control legislation?"

    a) In Texas, 1000 people are sampled; 402 answer YES. Give an estimate and margin of error for the percentage of all Texans who favor gun control legislation.

    b) In Wyoming another 1000 people are sampled; 378 answer YES. Give an estimate and margin of error for the percentage of all Montanans who favor gun control legislation.

    c) In New York 2000 people are sampled; 965 answer YES. Give an estimate and margin of error for the percentage of all New Yorkers who favor gun control legislation.

    d) What reliability is associated with each of your results?

    e) What are the approximate populations of Texas and Wyoming? (The answer can be found in the library or somewhere on the internet.)

    f) Compare the results from a, b and d. Does the margin of error depend on the size of the (state) population that is sampled from?

    g) The correct margin of error for the result in Texas is approximately ± 3.2%. A friend suggests that, since twice as many people are surveyed in New York, the margin of error ought to be twice as small…that is, the New York margin of error should be ± 1.6%. Is your friend right?

  3. A reporter for the Oswego newspaper surveys students at a local bar, asking them if they favor an earlier closing time for bars. Later the following headline is published: Only 20% of all students favor proposal for earlier closing of bars (margin of error ± 6%). What’s wrong here?

Solutions

  1. a) The population is all high school seniors. The sample is those high school seniors who were surveyed.
    b) The parameter is the percentage of all high school seniors who drink on a regular basis. The statistic is 30%, the percentage of the surveyed high school seniors who drink on a regular basis.
    c) 95%. Media polls come with an (unreported) 95% reliability or confidence.
    d) No. The interval given by the poll could, due to variability in random sampling, not include the desired result (the parameter).
    e) We don't know whether the result includes the true result (the parameter) in this particular poll. However, 95% of all polls are successful in this respect.
  2. a) 40.2% +/- 3.2%
    b) 37.8% +/- 3.2%
    c) 48.3% +/- 2.2%
    d) 95%
    e) Texas has a huge population. Wyoming's is comparatively small.
    f) Interestingly enough, the margin of error doesn't depend on the size of the population. (The results for Texas and Wyoming have the same margin of error.) It depends on the size of the sample.
    g) No. Doubling the sample size (1000 to 2000) doesn't halve the polling error -- the polling error shrinks from +/-3.2% to +/- 2.2%.
  3. Be very skeptical. Student's were not randomly sampled; in such a circumstance the reliability cannot be guaranteed to be 95%. In fact, this answer is most likely unreliable, as the sample was taken at a local bar where we'd most likely find the types of people who would be against earlier bar times (those people for earlier bar times will almost certainly not be included in the sample, as a result the sample is not random -- it is abiased sample).