Getting Started 
Misconception/Error The student is unable to use the sample data to estimate a population proportion. 
Examples of Student Work at this Level The student:
 Gives the number (10) or proportion (0.20 or its equivalent) of students in the survey who prefer horror movies.
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 Completes a computation unrelated to an estimate of a proportion.
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Questions Eliciting Thinking It looks like you found the number of students in the survey who prefer horror movies. Is this also your estimate of the number of students in the school who prefer horror movies?
It looks like you found (or approximated) the proportion of the students in the survey who prefer horror movies. How does this relate to the number of students in the school who prefer horror movies?
What did you calculate? Can you explain how it helps you estimate the proportion of students who prefer horror movies? 
Instructional Implications Clarify that the question is asking for an inference about a larger population from which the sample was drawn. Remind the student that the sample must be drawn in a way that increases the likelihood that it is representative of the population (e.g., the sample must be random and of adequate size). Explain that when sample data is used to estimate a population parameter, the term estimate is used because samples can vary. When using a sample statistic to generalize to a population, the outcome depends on the sample. Since sample statistics can vary, population parameters calculated from sample statistics will also vary. Consequently, these kinds of values are considered estimates of a population parameter. In addition, the actual population parameter is typically unknown so one never knows how close the estimate is. Be sure the student understands that there is no need to â€śestimateâ€ť or â€śapproximateâ€ť the sample statistic as this can be precisely calculated. Model how to calculate the proportion of students in the sample who prefer horror movies and how to use this proportion to estimate the number of students in the school who prefer horror movies. Emphasize that the estimate might be different if a different sample were drawn.
Discuss the source of variation in samples and explain that even when using good sampling procedures, some variation will result. Explain that the proportion of students preferring horror movies is likely to be different if another sample is drawn. Use a simulation to generate multiple samples and calculate a sample statistic for each. Show the student that there is variation in the sample statistic. Ask the student to describe the impact that this variation has on estimates of population parameters. 
Making Progress 
Misconception/Error The student does not understand sampling variability. 
Examples of Student Work at this Level The student calculates the sample proportion (0.20 or 20%) and uses it to estimate the number of students in the school who prefer horror movies (240). The student may say that another random sample from the same population will result in exactly the same or in a different outcome. However, the student does not indicate an understanding that the outcomes are likely to be similar although not precisely the same.
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Questions Eliciting Thinking Would you expect the results to be exactly the same if another sample is drawn?
How different do you think the results could be if another sample is drawn from the same population?
Would you expect the size of the sample to influence the results? 
Instructional Implications Discuss the source of variation in samples and explain that even when using good sampling procedures, some variation will result. However, the proportion of students preferring horror movies from many random samples should cluster around an average or mean proportion. Acknowledge that it is possible to get dramatically different results from repeated samples although it is less likely than getting similar results. Use a simulation to generate multiple samples and calculate the proportion of the same outcome for each sample. Ask the student to calculate the mean of the sample proportions. Discuss with the student that even though there is variation in the sample proportions, they tend to cluster around the mean of the sample proportions.
Provide additional opportunities to explore variations in sample statistics using simulations. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student calculates the sample proportion (0.20 or 20%) and uses it to estimate the number of students in the school who prefer horror movies (240). The student explains that if another random sample of students were drawn, the results are likely to be approximately the same but would probably be a little different due to sampling variability.
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Questions Eliciting Thinking What could you do to increase your confidence in this estimate of the number of students in the school who prefer horror movies?
Suppose you drew another random sample from the population of students. What impact might this have on your estimate of the number of students in the school who prefer horror movies? 
Instructional Implications Have the student use a simulation to generate multiple samples and calculate sample statistics. Ask the student to analyze the variation in the sample statistics and to describe its distribution. Then ask the student to calculate the mean of the sample statistics and compare it to the population parameter used to develop the simulation.
Consider using MFAS task School Days (7.SP.1.2). 