Evaluating Reports Based on Data
The Lesson Activities will help you meet these educational goals:
· Mathematical Practices—You will make sense of problems and solve them, reason abstractly and quantitatively, construct viable arguments and analyze the reasoning of others, and attend to precision.
· Inquiry—You will analyze results, communicate your results in written form, and draw conclusions.
· STEM—You will apply mathematical and technology tools and knowledge to analyze real-world situations and gain insight into careers in science, technology, engineering, and math.
· 21st Century Skills—You will use critical-thinking and problem-solving skills, communicate effectively, and assess and validate information.
Directions
You will evaluate some of these activities yourself, and your teacher may evaluate others. Please save this document before beginning the lesson and keep the document open for reference during the lesson. Type your answers directly in this document for all activities.
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Self-Checked Activities
Read the instructions for the following activities and type in your responses. At the end of the lesson, click the link to open the Student Answer Sheet. Use the answers or sample responses to evaluate your own work.
1. Analyzing Study Results
Read the Gallup college survey report.
a. In response to the first survey question (having a college degree essential for getting a good job), did most Americans agree, disagree, or neither agree nor disagree?
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b. How many individual people disagreed with the survey statement?
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c. In response to the second survey question (what is the main reason students get education beyond high school), was there a majority opinion?
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d. What percentage of respondents had an opinion other than those specified in the survey?
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e. Approximately how many of the 1,001 survey respondents neither agree nor disagree with the statement given in the third survey question (people with a college degree have a good chance of finding a quality job)?
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f. For the third survey question, what is the approximate ratio of people who strongly agree/agree to the number of people who strongly disagree/disagree? Round off your answer to two decimal places.
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g. Notice that for none of the three survey items are the respondents broken down into those who have a college degree and those who do not, nor are they broken down into those who have a good job and those who do not.
Do you think whether a person has a college degree or a good job would affect how he or she would answer these questions? Does not knowing the education level and employment status of the people answering the questions change your view on the validity of the survey results?
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How did you do? Check a box below.
Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.
Halfway There—I included most of the ideas in the model response on the Student Answer Sheet.
Not Great—I did not include any of the ideas in the model response on the Student Answer Sheet.
2. Analyzing Margin of Error
Read the Survey Methods section of the Gallup college survey report.
a. For the first survey item, determine the 95% confidence interval for those who responded “neither agree nor disagree.”
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b. Determine the 95% confidence interval for those who believe that earning more money was the main reason students get education beyond high school. (Ignore the “all of the above” option.)
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c. Determine the 95% confidence interval for those who disagreed that people who have a college degree have a better chance of getting a good job.
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d. The Survey Methods section of the report states, “For results based on the total sample size of 1,001 adults, one can say with 95% confidence that the margin of error attributable to sampling and other random effects is ±4 percentage points. For subgroups within this population, e.g., education level, gender, and income, the margin of error would be greater. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of opinion polls.” How does this information change how you might evaluate the report?
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How did you do? Check a box below.
Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.
Halfway There—I included most of the ideas in the model response on the Student Answer Sheet.
Not Great—I did not include any of the ideas in the model response on the Student Answer Sheet.
3. Constructing Confidence Intervals
Refer again to the Gallup college survey report, and answer these questions about the findings.
a. What is the standard error of proportion for the percentage of respondents who agree with the view that a college degree is essential for getting a good job?
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b. Construct the 68% confidence interval and the 99.7% confidence interval for those who agree that having a college degree is essential for getting a good job in this country.
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c. Construct the 68% confidence interval and the 99.7% confidence interval for those who believe that students opt for a college degree to get a good job. (Ignore the “all of the above” option.)
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d. Suppose that instead of giving a single percentage for each of the answers to the survey items, the report listed the 68%, 95%, and 99.7% confidence intervals. Do you think it would make the report better or worse?
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How did you do? Check a box below.
Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.
Halfway There—I included most of the ideas in the model response on the Student Answer Sheet.
Not Great—I did not include any of the ideas in the model response on the Student Answer Sheet.
4. Analyzing Survey Methods
Refer again to the Gallup college survey report and answer these questions.
a. Why do you think Gallup used a 5-point scale instead of a 3-point scale or a 10-point scale for the first and third survey questions?
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b. How did Gallup ensure that it got a random sample in the college degree survey?
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c. How would you evaluate the survey size? Do you think it was big enough? Why or why not?
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d. Make a judgment about this study. How could it have been better?
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e. Was it a good idea to combine categories in the first and third survey items?
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f. Do the percentages add up to 100% for each survey item? If no, what might be the reason?
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g. Evaluate the risks of having a category such as “All of the above” in the second survey item.
Type your response here:
How did you do? Check a box below.
Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.
Halfway There—I included most of the ideas in the model response on the Student Answer Sheet.
Not Great—I did not include any of the ideas in the model response on the Student Answer Sheet.
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