Classroom Resources (5) |

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 42 :

[MA2015] AL1 (9-12) 43 :

[MA2015] PRE (9-12) 45 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 47 :

[MA2015] PRE (9-12) 48 :

[MA2015] PRE (9-12) 40 :

[MA2015] PRE (9-12) 39 :

[MA2015] PRE (9-12) 41 :

42 ) Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [S-ID2]

[MA2015] AL1 (9-12) 43 :

43 ) Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3]

[MA2015] PRE (9-12) 45 :

45 ) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2]

Example: A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model'

[MA2015] PRE (9-12) 46 :

46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

[MA2015] PRE (9-12) 47 :

47 ) Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [S-IC4]

[MA2015] PRE (9-12) 48 :

48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

[MA2015] PRE (9-12) 40 :

40 ) Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (*Identify unifrom, skewed, and normal distridutions in a set of data. Determine the quartiles and interquartile range for a set of data.*) [S-ID3] (Alabama)

[MA2015] PRE (9-12) 39 :

39 ) Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. (*Focus on increasing rigor using standard deviation*). [S-ID2] (Alabama)

[MA2015] PRE (9-12) 41 :

41 ) Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4]

This exercise was developed to complement the film *The National Parks of Texas* by Texas PBS & Villita Media. In this activity, students will learn about estimating the number of trees in a large area based on a smaller area.

This is one way statisticians measure forests and other wide expanses of land. It's also a great way to illustrate how polling works. Scientists will interview a smaller sample size of Americans, rather than every single American, and then make estimations based on their results. In the same way, we counted smaller samples of trees, rather than all of the trees individually to get an estimate of how many trees are in the park total.

**Note: The corresponding lesson plan can be found under the "Support Materials for Teachers" link on the right side of the page. **

View Standards
**Standard(s): **
[MA2015] (7) 18 :

[MA2015] PRE (9-12) 45 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 48 :

[MA2015] PRE (9-12) 49 :

[MA2019] REG-7 (7) 10 :

18 ) Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7-SP2]

Example: Estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

[MA2015] PRE (9-12) 45 :

45 ) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2]

Example: A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model'

[MA2015] PRE (9-12) 46 :

46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

[MA2015] PRE (9-12) 48 :

48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

[MA2015] PRE (9-12) 49 :

49 ) Evaluate reports based on data. [S-IC6]

[MA2019] REG-7 (7) 10 :

10. Examine a sample of a population to generalize information about the population.

a. Differentiate between a sample and a population.

b. Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

c. Determine whether conclusions and generalizations can be made about a population based on a sample.

d. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and making predictions or conclusions about the population.

e. Informally explain situations in which statistical bias may exist.

[MA2019] REG-7 (7) 12 : 12. Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.

Statistics and sampling are important for human performance experiments. Students will learn several sampling types including census, random, stratified random, and convenience. Examples of real-life sampling and experimental design are also shown.

*Note: This video is available in both English and Spanish audio, along with corresponding closed captions.*

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 47 :

[MA2015] AL2 (9-12) 40 :

[MA2015] AL2 (9-12) 42 :

[MA2015] AL2 (9-12) 43 :

[MA2015] PRE (9-12) 45 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 48 :

[MA2015] PRE (9-12) 49 :

[MA2015] ALT (9-12) 44 :

[MA2015] ALT (9-12) 46 :

[MA2015] ALT (9-12) 47 :

47 ) Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [S-CP2]

[MA2015] AL2 (9-12) 40 :

40 ) Understand the conditional probability of *A* given *B* as *P*(*A* and *B*)/*P*(*B*), and interpret independence of *A* and *B* as saying that the conditional probability of *A* given *B* is the same as the probability of *A*, and the conditional probability of *B* given *A* is the same as the probability of *B*. [S-CP3]

[MA2015] AL2 (9-12) 42 :

42 ) Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [S-CP5]

Example: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

[MA2015] AL2 (9-12) 43 :

43 ) Find the conditional probability of *A* given *B* as the fraction of *B*'s outcomes that also belong to *A*, and interpret the answer in terms of the model. [S-CP6]

[MA2015] PRE (9-12) 45 :

45 ) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2]

Example: A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model'

[MA2015] PRE (9-12) 46 :

46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

[MA2015] PRE (9-12) 48 :

48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

[MA2015] PRE (9-12) 49 :

49 ) Evaluate reports based on data. [S-IC6]

[MA2015] ALT (9-12) 44 :

44 ) Understand the conditional probability of *A* given *B* as *P*(*A* and *B*)/*P*(*B*), and interpret independence of *A* and *B* as saying that the conditional probability of *A* given *B* is the same as the probability of *A*, and the conditional probability of *B* given *A* is the same as the probability of *B*. [S-CP3]

[MA2015] ALT (9-12) 46 :

46 ) Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [S-CP5]

Example: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

[MA2015] ALT (9-12) 47 :

47 ) Find the conditional probability of *A* given *B* as the fraction of *B*'s outcomes that also belong to *A*, and interpret the answer in terms of the model. [S-CP6]

Learn about the origins and meaning of “p-value,” a statistical measure of the probability that has become a benchmark for success in experimental science, in this video from NOVA: *Prediction by the Numbers*. In the 1920s and 1930s, British scientist Ronald A. Fisher laid out guidelines for designing experiments using statistics and probability to judge results. He proposed that if experimental results were due to chance alone, they would occur less than 5 percent (0.05) of the time. The lower the p-value, the less likely the experimental results were caused by chance. Use this resource to stimulate thinking and questions about the use of statistics and probability to test hypotheses and evaluate experimental results.

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 42 :

[MA2015] AL1 (9-12) 43 :

[MA2015] PRE (9-12) 44 :

[MA2015] PRE (9-12) 46 :46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

[MA2015] PRE (9-12) 48 :48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

[MA2015] PRE (9-12) 40 :

[MA2015] PRE (9-12) 39 :

42 ) Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [S-ID2]

[MA2015] AL1 (9-12) 43 :

43 ) Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3]

[MA2015] PRE (9-12) 44 :

44 ) Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [S-IC1]

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 48 :

[MA2015] PRE (9-12) 40 :

40 ) Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (*Identify unifrom, skewed, and normal distridutions in a set of data. Determine the quartiles and interquartile range for a set of data.*) [S-ID3] (Alabama)

[MA2015] PRE (9-12) 39 :

39 ) Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. (*Focus on increasing rigor using standard deviation*). [S-ID2] (Alabama)

Examine a mathematical theory known as the “wisdom of crowds,” which holds that a crowd’s predictive ability is greater than that of an individual, in this video from NOVA: *Prediction by the Numbers*. Sir Francis Galton documented this phenomenon after witnessing a weight-guessing contest more than a hundred years ago at a fair. Statistician Talithia Williams tests Galton’s theory with modern-day fairgoers, asking them to guess the number of jelly beans in a jar. Use this resource to stimulate thinking and questions about the use of statistics in everyday life and to make evidence-based claims about predictive ability.

View Standards
**Standard(s): **
[MA2015] PRE (9-12) 46 : 46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

[MA2015] PRE (9-12) 48 :48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

[MA2015] PRE (9-12) 49 :

[MA2015] PRE (9-12) 48 :

[MA2015] PRE (9-12) 49 :

49 ) Evaluate reports based on data. [S-IC6]

This topic focuses on drawing conclusions based on data from a statistical experiment. Experiments are introduced as investigations designed to compare the effect of two treatments on a response variable. Students revisit the distinction between random selection and random assignment.

When comparing two treatments using data from a statistical experiment, it is important to assess whether the observed difference in group means indicates a real difference between the treatments in the experiment or whether it is possible that there is no difference and that the observed difference is just a by-product of the random assignment of subjects to treatments (S-IC.B.5). To help students understand how this distinction is made, lessons in this topic use simulation to create a randomization distribution as a way of exploring the types of differences they might expect to see by chance when there is no real difference between groups. By understanding these differences, students are able to determine whether an observed difference in means is significant (S-IC.B.5).

Students also critique and evaluate published reports based on statistical experiments that compare two treatments (S-IC.B.6). For example, students read a short summary of an article in the online New England Journal of Medicine describing an experiment to determine if wearing a brace helps adolescents with scoliosis. Then, they watch an online video report for the Wall Street Journal titled “BMW Drivers Really Are Jerks” that describes a study of the relationship between driving behavior and the type of car driven.

**Note: Although this module is identified as Algebra II in the EngageNY curriculum, it corresponds to the Precalculus Alabama Course of Study.**