School Days

Getting Started

The student is unable to use the sample data to estimate a population parameter.

The student:

• Approximates the total number of students in the survey (about 90) who prefer longer school days.
  
  
  
  
  
  
  
  
• Approximates the proportion of students in the survey (about ) who prefer longer school days.
  
  
  
  
• Provides the sample proportion () rather than an estimate of the number of students in the school who prefer longer school days.
  
  

It looks like you approximated the number of students in the survey who prefer longer school days. Is this also your estimate of the number of students in the school who prefer longer school days?

It looks like you found (or approximated) the proportion of students in the survey who prefer longer school days. How does this relate to the number of students in the school who prefer longer school days?

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 unknown so one never knows how close the estimate is. Be sure the student understands that there is no need to “estimate” or “approximate” the sample statistic as this can be precisely calculated. Model how to calculate the proportion of students in the sample who prefer a longer school day and how to use this proportion to estimate the number of students in the school who prefer a longer school day. 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. Describe ways to increase the confidence in an estimate of a population parameter (e.g., use random samples that are of adequate size). Provide scenarios in which there are flaws in the sampling procedures and ask the student to identify them and suggest ways to improve them.

Making Progress

The student does not understand what can be done to increase the confidence in an estimate.

The student calculates the sample proportion and uses it to estimate the number of students in the school who prefer longer school days. However, the student is unable to describe a reasonable way to increase the confidence in the estimate.

What does it mean to increase the confidence in an estimate?

What could cause the sample results to be different from what is actually occurring in the population?

Discuss the source of variation in samples and explain that even when using good sampling procedures, some variation will result. Describe ways to increase the confidence in an estimate of a population parameter (e.g., use random samples that are of adequate size). Provide scenarios in which there are flaws in the sampling procedures and ask the student to identify them and suggest ways to improve them.

Got It

The student provides complete and correct responses to all components of the task.

The student calculates the sample proportion () and uses it to estimate the number of students in the school who prefer longer school days (1595). The student offers a reasonable suggestion for increasing the confidence in the estimate such as increasing the sample size.

Can you think of more than one way to increase the confidence in the estimate?

What would happen if another sample were drawn from the population of students? Would you expect the results to be the same as those for this sample?

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 identify any samples that appear to be outliers. 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 tasks Prediction Predicament and/or Movie Genre to further assess the student.